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Sample records for quantum-mechanical systems wavefunction

  1. Communication: Quantum mechanics without wavefunctions

    SciTech Connect

    Schiff, Jeremy; Poirier, Bill

    2012-01-21

    We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications--theoretical, computational, and interpretational--are discussed.

  2. Emergent quantum mechanics without wavefunctions

    NASA Astrophysics Data System (ADS)

    Mesa Pascasio, J.; Fussy, S.; Schwabl, H.; Grössing, G.

    2016-03-01

    We present our model of an Emergent Quantum Mechanics which can be characterized by “realism without pre-determination”. This is illustrated by our analytic description and corresponding computer simulations of Bohmian-like “surreal” trajectories, which are obtained classically, i.e. without the use of any quantum mechanical tool such as wavefunctions. However, these trajectories do not necessarily represent ontological paths of particles but rather mappings of the probability density flux in a hydrodynamical sense. Modelling emergent quantum mechanics in a high-low intesity double slit scenario gives rise to the “quantum sweeper effect” with a characteristic intensity pattern. This phenomenon should be experimentally testable via weak measurement techniques.

  3. Deterministic Impulsive Vacuum Foundations for Quantum-Mechanical Wavefunctions

    NASA Astrophysics Data System (ADS)

    Valentine, John S.

    2013-09-01

    By assuming that a fermion de-constitutes immediately at source, that its constituents, as bosons, propagate uniformly as scalar vacuum terms with phase (radial) symmetry, and that fermions are unique solutions for specific phase conditions, we find a model that self-quantizes matter from continuous waves, unifying bosons and fermion ontologies in a single basis, in a constitution-invariant process. Vacuum energy has a wavefunction context, as a mass-energy term that enables wave collapse and increases its amplitude, with gravitational field as the gradient of the flux density. Gravitational and charge-based force effects emerge as statistics without special treatment. Confinement, entanglement, vacuum statistics, forces, and wavefunction terms emerge from the model's deterministic foundations.

  4. Automatic computation of quantum-mechanical bound states and wavefunctions

    NASA Astrophysics Data System (ADS)

    Ledoux, V.; Van Daele, M.

    2013-04-01

    We discuss the automatic solution of the multichannel Schrödinger equation. The proposed approach is based on the use of a CP method for which the step size is not restricted by the oscillations in the solution. Moreover, this CP method turns out to form a natural scheme for the integration of the Riccati differential equation which arises when introducing the (inverse) logarithmic derivative. A new Prüfer type mechanism which derives all the required information from the propagation of the inverse of the log-derivative, is introduced. It improves and refines the eigenvalue shooting process and implies that the user may specify the required eigenvalue by its index. Catalogue identifier: AEON_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEON_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/license/license.html No. of lines in distributed program, including test data, etc.: 3822 No. of bytes in distributed program, including test data, etc.: 119814 Distribution format: tar.gz Programming language: Matlab. Computer: Personal computer architectures. Operating system: Windows, Linux, Mac (all systems on which Matlab can be installed). RAM: Depends on the problem size. Classification: 4.3. Nature of problem: Computation of eigenvalues and eigenfunctions of multichannel Schrödinger equations appearing in quantum mechanics. Solution method: A CP-based propagation scheme is used to advance the R-matrix in a shooting process. The shooting algorithm is supplemented by a Prüfer type mechanism which allows the eigenvalues to be computed according to index: the user specifies an integer k≥0, and the code computes an approximation to the kth eigenvalue. Eigenfunctions are also available through an auxiliary routine, called after the eigenvalue has been determined. Restrictions: The program can only deal with non-singular problems. Additional

  5. Quantum mechanics in complex systems

    NASA Astrophysics Data System (ADS)

    Hoehn, Ross Douglas

    This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown

  6. Quantum mechanics in complex systems

    NASA Astrophysics Data System (ADS)

    Hoehn, Ross Douglas

    This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown

  7. Quantum mechanical study of a generic quadratically coupled optomechanical system

    NASA Astrophysics Data System (ADS)

    Shi, H.; Bhattacharya, M.

    2013-04-01

    Typical optomechanical systems involving optical cavities and mechanical oscillators rely on a coupling that varies linearly with the oscillator displacement. However, recently a coupling varying instead as the square of the mechanical displacement has been realized, presenting new possibilities for nondemolition measurements and mechanical squeezing. In this article we present a quantum mechanical study of a generic quadratic-coupling optomechanical Hamiltonian. First, neglecting dissipation, we provide analytical results for the dressed states, spectrum, phonon statistics and entanglement. Subsequently, accounting for dissipation, we supply a numerical treatment using a master equation approach. We expect our results to be of use to optomechanical spectroscopy, state transfer, wave-function engineering, and entanglement generation.

  8. Calculation of wave-functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. Part I. Application of the Huzinaga equation.

    PubMed

    Ferenczy, György G

    2013-04-01

    Mixed quantum mechanics/quantum mechanics (QM/QM) and quantum mechanics/molecular mechanics (QM/MM) methods make computations feasible for extended chemical systems by separating them into subsystems that are treated at different level of sophistication. In many applications, the subsystems are covalently bound and the use of frozen localized orbitals at the boundary is a possible way to separate the subsystems and to ensure a sensible description of the electronic structure near to the boundary. A complication in these methods is that orthogonality between optimized and frozen orbitals has to be warranted and this is usually achieved by an explicit orthogonalization of the basis set to the frozen orbitals. An alternative to this approach is proposed by calculating the wave-function from the Huzinaga equation that guaranties orthogonality to the frozen orbitals without basis set orthogonalization. The theoretical background and the practical aspects of the application of the Huzinaga equation in mixed methods are discussed. Forces have been derived to perform geometry optimization with wave-functions from the Huzinaga equation. Various properties have been calculated by applying the Huzinaga equation for the central QM subsystem, representing the environment by point charges and using frozen strictly localized orbitals to connect the subsystems. It is shown that a two to three bond separation of the chemical or physical event from the frozen bonds allows a very good reproduction (typically around 1 kcal/mol) of standard Hartree-Fock-Roothaan results. The proposed scheme provides an appropriate framework for mixed QM/QM and QM/MM methods.

  9. Calculation of wave-functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. Part I. Application of the Huzinaga equation.

    PubMed

    Ferenczy, György G

    2013-04-01

    Mixed quantum mechanics/quantum mechanics (QM/QM) and quantum mechanics/molecular mechanics (QM/MM) methods make computations feasible for extended chemical systems by separating them into subsystems that are treated at different level of sophistication. In many applications, the subsystems are covalently bound and the use of frozen localized orbitals at the boundary is a possible way to separate the subsystems and to ensure a sensible description of the electronic structure near to the boundary. A complication in these methods is that orthogonality between optimized and frozen orbitals has to be warranted and this is usually achieved by an explicit orthogonalization of the basis set to the frozen orbitals. An alternative to this approach is proposed by calculating the wave-function from the Huzinaga equation that guaranties orthogonality to the frozen orbitals without basis set orthogonalization. The theoretical background and the practical aspects of the application of the Huzinaga equation in mixed methods are discussed. Forces have been derived to perform geometry optimization with wave-functions from the Huzinaga equation. Various properties have been calculated by applying the Huzinaga equation for the central QM subsystem, representing the environment by point charges and using frozen strictly localized orbitals to connect the subsystems. It is shown that a two to three bond separation of the chemical or physical event from the frozen bonds allows a very good reproduction (typically around 1 kcal/mol) of standard Hartree-Fock-Roothaan results. The proposed scheme provides an appropriate framework for mixed QM/QM and QM/MM methods. PMID:23281055

  10. Calculation of wave-functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. II. Application of the local basis equation.

    PubMed

    Ferenczy, György G

    2013-04-01

    The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009, 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self-consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree-Fock-Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self-consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave-function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem.

  11. The exact wavefunction factorization of a vibronic coupling system

    SciTech Connect

    Chiang, Ying-Chih; Klaiman, Shachar; Otto, Frank; Cederbaum, Lorenz S.

    2014-02-07

    We investigate the exact wavefunction as a single product of electronic and nuclear wavefunction for a model conical intersection system. Exact factorized spiky potentials and nodeless nuclear wavefunctions are found. The exact factorized potential preserves the symmetry breaking effect when the coupling mode is present. Additionally nodeless wavefunctions are found to be closely related to the adiabatic nuclear eigenfunctions. This phenomenon holds even for the regime where the non-adiabatic coupling is relevant, and sheds light on the relation between the exact wavefunction factorization and the adiabatic approximation.

  12. Scalable quantum mechanical simulation of large polymer systems

    SciTech Connect

    Goedecker, S.; Hoisie, A.; Kress, J.; Lubeck, O.; Wasserman, H.

    1997-08-01

    We describe a program for quantum mechanical calculations of very large hydrocarbon polymer systems. It is based on a new algorithmic approach to the quantum mechanical tight binding equations that naturally leads to a very efficient parallel implementation and that scales linearly with respect to the number of atoms. We get both very high single node performance as well as a significant parallel speedup on the SGI Origin 2000 parallel computer.

  13. Semiclassical modeling of quantum-mechanical multiparticle systems using parallel particle-in-cell methods

    NASA Astrophysics Data System (ADS)

    Dauger, Dean Edward

    2001-08-01

    We are successful in building a code that models many particle dynamic quantum systems by combining a semiclassical approximation of Feynman path integrals with parallel computing techniques (particle-in-cell) and numerical methods developed for simulating plasmas, establishing this approach as a viable technique for multiparticle time-dependent quantum mechanics. Run on high-performance parallel computers, this code applies semiclassical methods to simulate the time evolution of wavefunctions of many particles. We describe the analytical derivation and computational implementation of these techniques in detail. We present a study to thoroughly demonstrate the code's fidelity to quantum mechanics, resulting in innovative visualization and analysis techniques. We introduce and exhibit a method to address fermion particle statistics. We present studies of two quantum-mechanical problems: a two-electron, one- dimensional atom, resulting in high-quality extractions of one- and two-electron eigenstates, and electrostatic quasi-modes due to quantum effects in a hot electron plasma, relevant for predictions about stellar evolution. We supply discussions of alternative derivations, alternative implementations of the derivations, and an exploration of their consequences. Source code is shown throughout this dissertation. Finally, we present an extensive discussion of applications and extrapolations of this work, with suggestions for future direction.

  14. Wavefunction controllability for finite-dimensional bilinear quantum systems

    NASA Astrophysics Data System (ADS)

    Turinici, Gabriel; Rabitz, Herschel

    2003-03-01

    We present controllability results for quantum systems interacting with lasers. Exact controllability for the wavefunction in these bilinear systems is proved in the finite-dimensional case under very natural hypotheses.

  15. Contexts, Systems and Modalities: A New Ontology for Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Auffèves, Alexia; Grangier, Philippe

    2016-02-01

    In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules. Rather than elaborating on the quantum formalism itself, we propose a new quantum ontology, where physical properties are attributed jointly to the system, and to the context in which it is embedded. In combination with a quantization principle, this non-classical definition of physical reality sheds new light on counter-intuitive features of quantum mechanics such as the origin of probabilities, non-locality, and the quantum-classical boundary.

  16. Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Auletta, Gennaro; Fortunato, Mauro; Parisi, Giorgio

    2014-01-01

    Introduction; Part I. Basic Features of Quantum Mechanics: 1. From classical mechanics to quantum mechanics; 2. Quantum observable and states; 3. Quantum dynamics; 4. Examples of quantum dynamics; 5. Density matrix; Part II. More Advanced Topics: 6. Angular momentum and spin; 7. Identical particles; 8. Symmetries and conservation laws; 9. The measurement problem; Part III. Matter and Light: 10. Perturbations and approximation methods; 11. Hydrogen and helium atoms; 12. Hydrogen molecular ion; 13. Quantum optics; Part IV. Quantum Information: State and Correlations: 14. Quantum theory of open systems; 15. State measurement in quantum mechanics; 16. Entanglement: non-separability; 17. Entanglement: quantum information; References; Index.

  17. Why irreversibility? The formulation of classical and quantum mechanics for nonintegrable systems

    SciTech Connect

    Prigogine, I.

    1995-01-05

    Nonintegrable Poincare systems with a continuous spectrum lead to the appearance of diffusive terms in the frame of classical or quantum dynamics. These terms break time symmetry. They lead, therefore, to limitations to classical trajectory theory and of wave-function formalism. These diffusive terms correspond to well-defined classes of dynamical processes. The diffusive effects are amplified in situations corresponding to persistent interactions. As a result, we have to include, already, in the fundamental dynamical description the two basic aspects, probability and irreversibility, which are so conspicuous on the macroscopic level. We have to formulate both classical and quantum mechanics on the Liouville level of probability distributions. For integrable systems, we recover the usual formulation of classical or quantum mechanics. Instead of being primitive concepts, which cannot be further analyzed, trajectories and wave functions appear as special solutions of the Liouville-von Neumann equations. This extension of classical and quantum dynamics permits us to unify the two concepts of nature that we inherited from the nineteenth century, based, on the one hand, on dynamical time-reversible laws and, on the other, on an evolutionary view associated to entropy. It leads also to a unified formulation of quantum theory, avoiding the conventional dual structure based on Schroedinger`s equation, on the one hand, and on the {open_quotes}collapse{close_quotes} of the wave function, on the other. A dynamical interpretation is given to processes such as decoherence or approach to equilibrium without any appeal to extra dynamic considerations. There is a striking parallelism between classical and quantum theory. For large Poincare systems (LPS), we have, in general, both a {open_quotes}collapse{close_quotes} of trajectories and of wave functions. In both cases, we need a generalized formulation of dynamics in terms of probability distributions or density matrices.

  18. Conservation laws in the quantum mechanics of closed systems

    SciTech Connect

    Hartle, J.B. ||; Laflamme, R. |; Marolf, D.

    1995-06-15

    We investigate conservation laws in the quantum mechanics of closed systems and begin by reviewing an argument that exact decoherence implies the exact conservation of quantities that commute with the Hamiltonian. However, we also show that decoherence limits the alternatives that can be included in sets of histories that assess the conservation of these quantities. In the case of charge and energy, these limitations would be severe were these quantities not coupled to a gauge field. However, for the realistic cases of electric charge coupled to the electromagnetic field and mass coupled to spacetime curvature, we show that when alternative values of charge and mass decohere they always decohere exactly and are exactly conserved. Further, while decohering histories that describe possible changes in time of the total charge and mass are also subject to the limitations mentioned above, we show that these do not, in fact, restrict {ital physical} alternatives and are therefore not really limitations at all.

  19. Self-Referential Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Mitchell, Mark Kenneth

    1993-01-01

    A nonlinear quantum mechanics based upon the nonlinear logarithmic Schrodinger equation, is developed which has the property of self-reference, that is, the nonlinear term is dependent upon the square of the wavefunction. The self-referential system is examined in terms of its mathematical properties, the definition of the wavefunction, and the nonlinear system in the feedback between equation and solution. Theta operators are introduced which make possible new operations in the quantum phase. Two interpretations are presented utilizing the nonlinear quantum system: the idealistic interpretation based upon consciousness focused upon the measurement problem, and the statistical interpretation focused upon stochastic quantum fluctuations. Experimental properties are examined, beginning with a proposed analog of the Bohm-Aharonov experiment. Interference due to difference in path length for a split electron beam is effected in a region of spacetime where electromagnetic field and the vector potential are enclosed within but screened to be zero at the paths. If the wavefunction's geometrical phase contribution along the paths is different, then there should be interference induced purely by the wave-function alone. A positive result would be due to a purely wavefunction dependent effect. The spin phase of the wavefunction is postulated to be the source of the zitterbewegung of the electron. Reduction of the wavefunction in measurement is examined for self -referential quantum systems arising from consciousness and then arising from a stochastic quantum spacetime model. These results are applied to the mind-brain as a quantum processor producing a behavioral double slit experiment (ideation experiments) and nonlocal transferred potentials in an EPR-style experiment. Looking at the universe as a whole as a quantum self-referential system, leads to a modified zitterbewegung Wheeler-DeWitt equation; and, the transition from quantum-to-classical on a cosmological scale for

  20. Tampering detection system using quantum-mechanical systems

    DOEpatents

    Humble, Travis S.; Bennink, Ryan S.; Grice, Warren P.

    2011-12-13

    The use of quantum-mechanically entangled photons for monitoring the integrity of a physical border or a communication link is described. The no-cloning principle of quantum information science is used as protection against an intruder's ability to spoof a sensor receiver using a `classical` intercept-resend attack. Correlated measurement outcomes from polarization-entangled photons are used to protect against quantum intercept-resend attacks, i.e., attacks using quantum teleportation.

  1. Quantum mechanical molecular dynamics studies of chemical systems

    NASA Astrophysics Data System (ADS)

    Pavese, Marc

    Methods for including quantum mechanical effects in molecular dynamics (MD) simulations are discussed in this thesis. The thesis focuses on the path integral centroid molecular dynamics (CMD) algorithm. This algorithm is first described and then used in simulations of low temperature para-hydrogen, and also in simulations of the excess proton in water clusters and in the bulk. The CMD method allows one to include the effects of nuclear quantization approximately while still maintaining a quasi-classical, trajectory based, description of the dynamics. The effects of quantization of the electronic degrees of freedom are also discussed. These effects are usually taken into account implicitly through parameterized potential functions. However, methods for including the quantum electronic degrees of freedom explicitly in a MD simulation are also discussed in this thesis. Most notably, the Car-Parrinello method, which combines density functional theory (DFT) with MD, is employed with the CMD algorithm. This yields a method which takes explicit account of the quantum electrons and nuclei. Thus, this work represents one feasible approach for considering the quantum nature of all the degrees of freedom of the system while still maintaining an MD framework. In the concluding remarks, future directions and possibilities for this type of approach are discussed.

  2. Quantum-mechanical transport equation for atomic systems.

    NASA Technical Reports Server (NTRS)

    Berman, P. R.

    1972-01-01

    A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

  3. Nontrivial systems and the necessity of the scalar quantum mechanics axioms

    SciTech Connect

    Kotulek, Jan

    2009-06-15

    We discuss the necessity of the axioms of scalar quantum mechanics introduced by Paschke and clearly demonstrate their geometric and/or physical meaning. We show that reasonable nonrelativistic quantum mechanics is exactly specified by the axioms. A system describing the electric Aharonov-Bohm effect is presented. It illustrates the topological obstructions for the existence of a Hamiltonian.

  4. Using quantum mechanical approaches to study biological systems.

    PubMed

    Merz, Kenneth M

    2014-09-16

    Conspectus Quantum mechanics (QM) has revolutionized our understanding of the structure and reactivity of small molecular systems. Given the tremendous impact of QM in this research area, it is attractive to believe that this could also be brought into the biological realm where systems of a few thousand atoms and beyond are routine. Applying QM methods to biological problems brings an improved representation to these systems by the direct inclusion of inherently QM effects such as polarization and charge transfer. Because of the improved representation, novel insights can be gleaned from the application of QM tools to biomacromolecules in aqueous solution. To achieve this goal, the computational bottlenecks of QM methods had to be addressed. In semiempirical theory, matrix diagonalization is rate limiting, while in density functional theory or Hartree-Fock theory electron repulsion integral computation is rate-limiting. In this Account, we primarily focus on semiempirical models where the divide and conquer (D&C) approach linearizes the matrix diagonalization step with respect to the system size. Through the D&C approach, a number of applications to biological problems became tractable. Herein, we provide examples of QM studies on biological systems that focus on protein solvation as viewed by QM, QM enabled structure-based drug design, and NMR and X-ray biological structure refinement using QM derived restraints. Through the examples chosen, we show the power of QM to provide novel insights into biological systems, while also impacting practical applications such as structure refinement. While these methods can be more expensive than classical approaches, they make up for this deficiency by the more realistic modeling of the electronic nature of biological systems and in their ability to be broadly applied. Of the tools and applications discussed in this Account, X-ray structure refinement using QM models is now generally available to the community in the

  5. Measurements on the reality of the wavefunction

    NASA Astrophysics Data System (ADS)

    Ringbauer, M.; Duffus, B.; Branciard, C.; Cavalcanti, E. G.; White, A. G.; Fedrizzi, A.

    2015-03-01

    Quantum mechanics is an outstandingly successful description of nature, underpinning fields from biology through chemistry to physics. At its heart is the quantum wavefunction, the central tool for describing quantum systems. Yet it is still unclear what the wavefunction actually is: does it merely represent our limited knowledge of a system, or is it in direct correspondence to reality? Recent no-go theorems argued that if there was any objective reality, then the wavefunction must be real. However, that conclusion relied on debatable assumptions. Here we follow a different approach without these assumptions and experimentally bound the degree to which knowledge interpretations can explain quantum phenomena. Using single photons, we find that no knowledge interpretation can fully explain the limited distinguishability of non-orthogonal quantum states in three and four dimensions. Assuming that a notion of objective reality exists, our results thus strengthen the view that the wavefunction should directly correspond to this reality.

  6. Can We Describe Biological Systems with Quantum Mechanics?

    NASA Astrophysics Data System (ADS)

    Granados-Ramírez, C. G.; Benítez-Cardoza, C. G.; Carbajal-Tinoco, M. D.

    2016-03-01

    Quantum Mechanics is the favourite theory to predict the structure of any group of atoms, including biological molecules. Due to numerous difficulties, however, it is necessary to introduce a series of approximations to overcome such impediments. We present a coarse-grained model of circular dichroism (CD) that is based on the theory of optical activity, developed by DeVoe, in order to predict CD spectra. In first stage, we determine the polarisability of individual monomers (residues, in the case of peptides) from experiments of molar absorptivity. The complex polarisabilities are used together with peptide structures obtained by density functional theory and other methods to determine their corresponding CD spectra, which are in reasonable agreement with their experimental counterparts.

  7. Independent bases on the spatial wavefunction of four-identical-particle systems

    SciTech Connect

    Xiao, Shuyuan; Deng, Zhixuan; Chen, Hong

    2013-12-15

    We construct the independent bases on the spatial wavefunction of four-identical-particle systems classified under the rotational group SO(3) and the permutation group S{sub 4} with the usage of transformation coefficients that relate wavefunctions described in one set of internal coordinates with those in another. The basis functions for N⩽ 2 are presented in the explicit expressions based on the harmonic oscillator model. Such independent bases are supposed to play a key role in the construction of the wavefunctions of the five-quark states and the variation calculation of four-body systems. Our prescription avoids the spurious states and can be programmed for arbitrary N.

  8. quantum mechanics

    PubMed Central

    Bender, Carl M; DeKieviet, Maarten; Klevansky, S. P.

    2013-01-01

    -symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter–antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantum mechanics. PMID:23509390

  9. Quantum mechanics without potential function

    SciTech Connect

    Alhaidari, A. D.; Ismail, M. E. H.

    2015-07-15

    In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schrödinger equation, which is solved for the wavefunction, bound states energy spectrum, and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which is written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states, and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and three-parameter systems.

  10. Non-Hermitian quantum mechanics and localization in physical systems

    SciTech Connect

    Hatano, Naomichi

    1998-12-31

    Recent studies on a delocalization phenomenon of a non-Hermitian random system is reviewed. The complex spectrum of the system indicates delocalization transition of its eigenfunctions. It is emphasized that the delocalization is related to various physical phenomena such as flux-line pinning in superconductors and population biology of bacteria colony.

  11. Entanglement in algebraic quantum mechanics: Majorana fermion systems

    NASA Astrophysics Data System (ADS)

    Benatti, F.; Floreanini, R.

    2016-07-01

    Many-body entanglement is studied within the algebraic approach to quantum physics in systems made of Majorana fermions. In this framework, the notion of separability stems from partitions of the algebra of observables and properties of the associated correlation functions, rather than on particle tensor products. This allows a complete characterization of non-separable Majorana fermion states to be obtained. These results may have direct application in quantum metrology: using Majorana systems, sub-shot-noise accuracy in parameter estimations can be achieved without preliminary resource-consuming, state entanglement operations.

  12. The quantum mechanics of cosmology.

    NASA Astrophysics Data System (ADS)

    Hartle, James B.

    The following sections are included: * INTRODUCTION * POST-EVERETT QUANTUM MECHANICS * Probability * Probabilities in general * Probabilities in Quantum Mechanics * Decoherent Histories * Fine and Coarse Grained Histories * Decohering Sets of Coarse Grained Histories * No Moment by Moment Definition of Decoherence * Prediction, Retrodiction, and History * Prediction and Retrodiction * The Reconstruction of History * Branches (Illustrated by a Pure ρ) * Sets of Histories with the Same Probabilities * The Origins of Decoherence in Our Universe * On What Does Decoherence Depend? * Two Slit Model * The Caldeira-Leggett Oscillator Model * The Evolution of Reduced Density Matrices * Towards a Classical Domain * The Branch Dependence of Decoherence * Measurement * The Ideal Measurement Model and the Copenhagen Approximation to Quantum Mechanics * Approximate Probabilities Again * Complex Adaptive Systems * Open Questions * GENERALIZED QUANTUM MECHANICS * General Features * Hamiltonian Quantum Mechanics * Sum-Over-Histories Quantum Mechanics for Theories with a Time * Differences and Equivalences between Hamiltonian and Sum-Over-Histories Quantum Mechanics for Theories with a Time * Classical Physics and the Classical Limit of Quantum Mechanics * Generalizations of Hamiltonian Quantum Mechanics * TIME IN QUANTUM MECHANICS * Observables on Spacetime Regions * The Arrow of Time in Quantum Mechanics * Topology in Time * The Generality of Sum Over Histories Quantum Mechanics * THE QUANTUM MECHANICS OF SPACETIME * The Problem of Time * General Covariance and Time in Hamiltonian Quantum Mechanics * The "Marvelous Moment" * A Quantum Mechanics for Spacetime * What we Need * Sum-Over-Histories Quantum Mechanics for Theories Without a Time * Sum-Over-Spacetime-Histories Quantum Mechanics * Extensions and Contractions * The Construction of Sums Over Spacetime Histories * Some Open Questions * PRACTICAL QUANTUM COSMOLOGY * The Semiclassical Regime * The Semiclassical Approximation

  13. Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Mandl, F.

    1992-07-01

    The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Quantum Mechanics aims to teach those parts of the subject which every physicist should know. The object is to display the inherent structure of quantum mechanics, concentrating on general principles and on methods of wide applicability without taking them to their full generality. This book will equip students to follow quantum-mechanical arguments in books and scientific papers, and to cope with simple cases. To bring the subject to life, the theory is applied to the all-important field of atomic physics. No prior knowledge of quantum mechanics is assumed. However, it would help most readers to have met some elementary wave mechanics before. Primarily written for students, it should also be of interest to experimental research workers who require a good grasp of quantum mechanics without the full formalism needed by the professional theorist. Quantum Mechanics features: A flow diagram allowing topics to be studied in different orders or omitted altogether. Optional "starred" and highlighted sections containing more advanced and specialized material for the more ambitious reader. Sets of problems at the end of each chapter to help student understanding. Hints and solutions to the problems are given at the end of the book.

  14. Is quantum mechanics exact?

    NASA Astrophysics Data System (ADS)

    Kapustin, Anton

    2013-06-01

    We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.

  15. Is quantum mechanics exact?

    SciTech Connect

    Kapustin, Anton

    2013-06-15

    We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.

  16. Optimal guidance law in quantum mechanics

    SciTech Connect

    Yang, Ciann-Dong Cheng, Lieh-Lieh

    2013-11-15

    Following de Broglie’s idea of a pilot wave, this paper treats quantum mechanics as a problem of stochastic optimal guidance law design. The guidance scenario considered in the quantum world is that an electron is the flight vehicle to be guided and its accompanying pilot wave is the guidance law to be designed so as to guide the electron to a random target driven by the Wiener process, while minimizing a cost-to-go function. After solving the stochastic optimal guidance problem by differential dynamic programming, we point out that the optimal pilot wave guiding the particle’s motion is just the wavefunction Ψ(t,x), a solution to the Schrödinger equation; meanwhile, the closed-loop guidance system forms a complex state–space dynamics for Ψ(t,x), from which quantum operators emerge naturally. Quantum trajectories under the action of the optimal guidance law are solved and their statistical distribution is shown to coincide with the prediction of the probability density function Ψ{sup ∗}Ψ. -- Highlights: •Treating quantum mechanics as a pursuit-evasion game. •Reveal an interesting analogy between guided flight motion and guided quantum motion. •Solve optimal quantum guidance problem by dynamic programming. •Gives a formal proof of de Broglie–Bohm’s idea of a pilot wave. •The optimal pilot wave is shown to be a wavefunction solved from Schrödinger equation.

  17. Process, System, Causality, and Quantum Mechanics: A Psychoanalysis of Animal Faith

    NASA Astrophysics Data System (ADS)

    Etter, Tom; Noyes, H. Pierre

    We shall argue in this paper that a central piece of modern physics does not really belong to physics at all but to elementary probability theory. Given a joint probability distribution J on a set of random variables containing x and y, define a link between x and y to be the condition x=y on J. Define the {\\it state} D of a link x=y as the joint probability distribution matrix on x and y without the link. The two core laws of quantum mechanics are the Born probability rule, and the unitary dynamical law whose best known form is the Schrodinger's equation. Von Neumann formulated these two laws in the language of Hilbert space as prob(P) = trace(PD) and D'T = TD respectively, where P is a projection, D and D' are (von Neumann) density matrices, and T is a unitary transformation. We'll see that if we regard link states as density matrices, the algebraic forms of these two core laws occur as completely general theorems about links. When we extend probability theory by allowing cases to count negatively, we find that the Hilbert space framework of quantum mechanics proper emerges from the assumption that all D's are symmetrical in rows and columns. On the other hand, Markovian systems emerge when we assume that one of every linked variable pair has a uniform probability distribution. By representing quantum and Markovian structure in this way, we see clearly both how they differ, and also how they can coexist in natural harmony with each other, as they must in quantum measurement, which we'll examine in some detail. Looking beyond quantum mechanics, we see how both structures have their special places in a much larger continuum of formal systems that we have yet to look for in nature.

  18. Nonlinear quantum-mechanical system associated with Sine-Gordon equation in (1 + 2) dimensions

    SciTech Connect

    Zarmi, Yair

    2014-10-15

    Despite the fact that it is not integrable, the (1 + 2)-dimensional Sine-Gordon equation has N-soliton solutions, whose velocities are lower than the speed of light (c = 1), for all N ≥ 1. Based on these solutions, a quantum-mechanical system is constructed over a Fock space of particles. The coordinate of each particle is an angle around the unit circle. U, a nonlinear functional of the particle number-operators, which obeys the Sine-Gordon equation in (1 + 2) dimensions, is constructed. Its eigenvalues on N-particle states in the Fock space are the slower-than-light, N-soliton solutions of the equation. A projection operator (a nonlinear functional of U), which vanishes on the single-particle subspace, is a mass-density generator. Its eigenvalues on multi-particle states play the role of the mass density of structures that emulate free, spatially extended, relativistic particles. The simplicity of the quantum-mechanical system allows for the incorporation of perturbations with particle interactions, which have the capacity to “annihilate” and “create” solitons – an effect that does not have an analog in perturbed classical nonlinear evolution equations.

  19. Quantum mechanical origin of the plasmon: from molecular systems to nanoparticles.

    PubMed

    Guidez, Emilie B; Aikens, Christine M

    2014-10-21

    The surface plasmon resonance (SPR) of noble metal nanoparticles is reviewed in terms of both classical and quantum mechanical approaches. The collective oscillation of the free electrons responsible for the plasmon is well described using classical electromagnetic theory for large systems (from about 10 to 100 nm). In cases where quantum effects are important, this theory fails and first principle approaches like time-dependent density functional theory (TDDFT) must be used. In this paper, we give an account of the current understanding of the quantum mechanical origin of plasmon resonances. We provide some insight into how the discrete absorption spectrum of small noble metal clusters evolves into a strong plasmon peak with increasing particle size. The collective character of the plasmon is described in terms of the constructive addition of single-particle excitations. As the system size increases, the number of single-particle excitations increases as well. A configuration interaction (CI) approach can be applied to describe the optical properties of particles of all shapes and sizes, providing a consistent definition of plasmon resonances. Finally, we expand our analysis to thiolate-protected nanoparticles and analyze the effects of ligands on the plasmon.

  20. Particles, Waves, and the Interpretation of Quantum Mechanics

    ERIC Educational Resources Information Center

    Christoudouleas, N. D.

    1975-01-01

    Presents an explanation, without mathematical equations, of the basic principles of quantum mechanics. Includes wave-particle duality, the probability character of the wavefunction, and the uncertainty relations. (MLH)

  1. Phase space quantum mechanics

    NASA Astrophysics Data System (ADS)

    Błaszak, Maciej; Domański, Ziemowit

    2012-02-01

    This paper develops an alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise product of observables to an appropriate noncommutative ⋆-product and the deformation of the Poisson bracket to an appropriate Lie bracket are the key elements in introducing the quantization of classical Hamiltonian systems. The formalism of the phase space quantum mechanics is presented in a very systematic way for the case of any smooth Hamiltonian function and for a very wide class of deformations. The considered class of deformations and the corresponding ⋆-products contains as a special case all deformations which can be found in the literature devoted to the subject of the phase space quantum mechanics. Fundamental properties of ⋆-products of observables, associated with the considered deformations are presented as well. Moreover, a space of states containing all admissible states is introduced, where the admissible states are appropriate pseudo-probability distributions defined on the phase space. It is proved that the space of states is endowed with a structure of a Hilbert algebra with respect to the ⋆-multiplication. The most important result of the paper shows that developed formalism is more fundamental than the axiomatic ordinary quantum mechanics which appears in the presented approach as the intrinsic element of the general formalism. The equivalence of two formulations of quantum mechanics is proved by observing that the Wigner-Moyal transform has all properties of the tensor product. This observation allows writing many previous results found in the literature in a transparent way, from which the equivalence of the two formulations of quantum mechanics follows naturally. In addition, examples of a free particle and a simple harmonic

  2. Noncommutative quantum mechanics

    NASA Astrophysics Data System (ADS)

    Gamboa, J.; Loewe, M.; Rojas, J. C.

    2001-09-01

    A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.

  3. Incoherent control of quantum systems with wavefunction-controllable subspaces via quantum reinforcement learning.

    PubMed

    Dong, Daoyi; Chen, Chunlin; Tarn, Tzyh-Jong; Pechen, Alexander; Rabitz, Herschel

    2008-08-01

    In this paper, an incoherent control scheme for accomplishing the state control of a class of quantum systems which have wavefunction-controllable subspaces is proposed. This scheme includes the following two steps: projective measurement on the initial state and learning control in the wavefunction-controllable subspace. The first step probabilistically projects the initial state into the wavefunction-controllable subspace. The probability of success is sensitive to the initial state; however, it can be greatly improved through multiple experiments on several identical initial states even in the case with a small probability of success for an individual measurement. The second step finds a local optimal control sequence via quantum reinforcement learning and drives the controlled system to the objective state through a set of suitable controls. In this strategy, the initial states can be unknown identical states, the quantum measurement is used as an effective control, and the controlled system is not necessarily unitarily controllable. This incoherent control scheme provides an alternative quantum engineering strategy for locally controllable quantum systems.

  4. Testing Quantum Mechanics using a Triple slit experiment

    NASA Astrophysics Data System (ADS)

    Sinha, Urbasi; Couteau, Christophe; Jennewein, Thomas; Sorkin, Rafael; Laflamme, Raymond; Weihs, Gregor

    2010-03-01

    As one of the postulates of quantum mechanics, Born's rule tells us how to get probabilities for experimental outcomes from the complex wavefunction of the system. It's quadratic nature entails that interference occurs in pairs of paths. An experiment is in progress in our laboratory that sets out to test the correctness of Born's rule by testing for the presence or absence of genuine three-path interference [1]. This is done using single photons and a three slit aperture. Although the Born rule has been indirectly verified to high accuracy in other experiments, the consequences of a detection of even a small three-way interference in the Quantum mechanical null prediction are tremendous. If a non-zero result were to be obtained, it would mean that Quantum Mechanics is only approximate, in the same way that the double slit experiment proves that classical physics is only an approximation to the true law of nature. This would give us an important hint on how to generalize Quantum Mechanics and open a new window to the world. Some preliminary observations have been reported in reference [2]. In this talk, I will show results that bound the possible violation of the second sum rule and will point out ways to obtain a tighter experimental bound. [1] R. D. Sorkin, Mod. Phys. Lett. A 9, 3119 (1994). [2] U. Sinha et al, in Foundations of Probability and Physics-5, A I P Conference Proceedings, Vol. 1101, pp. 200-207, New-York (2009)

  5. Quantum wavefunction controllability

    NASA Astrophysics Data System (ADS)

    Turinici, Gabriel; Rabitz, Herschel

    2001-06-01

    Theoretical results are presented on the ability to arbitrarily steer about a wavefunction for a quantum system under time-dependent external field control. Criteria on the field free Hamiltonian and the field coupling term in the Hamiltonian are presented that assure full wavefunction controllability. Numerical simulations are given to illustrate the criteria. A discussion on the theoretical and practical relationship between dynamical conservation laws and controllability is also included.

  6. A quantum-mechanics molecular-mechanics scheme for extended systems.

    PubMed

    Hunt, Diego; Sanchez, Veronica M; Scherlis, Damián A

    2016-08-24

    We introduce and discuss a hybrid quantum-mechanics molecular-mechanics (QM-MM) approach for Car-Parrinello DFT simulations with pseudopotentials and planewaves basis, designed for the treatment of periodic systems. In this implementation the MM atoms are considered as additional QM ions having fractional charges of either sign, which provides conceptual and computational simplicity by exploiting the machinery already existing in planewave codes to deal with electrostatics in periodic boundary conditions. With this strategy, both the QM and MM regions are contained in the same supercell, which determines the periodicity for the whole system. Thus, while this method is not meant to compete with non-periodic QM-MM schemes able to handle extremely large but finite MM regions, it is shown that for periodic systems of a few hundred atoms, our approach provides substantial savings in computational times by treating classically a fraction of the particles. The performance and accuracy of the method is assessed through the study of energetic, structural, and dynamical aspects of the water dimer and of the aqueous bulk phase. Finally, the QM-MM scheme is applied to the computation of the vibrational spectra of water layers adsorbed at the TiO2 anatase (1 0 1) solid-liquid interface. This investigation suggests that the inclusion of a second monolayer of H2O molecules is sufficient to induce on the first adsorbed layer, a vibrational dynamics similar to that taking place in the presence of an aqueous environment. The present QM-MM scheme appears as a very interesting tool to efficiently perform molecular dynamics simulations of complex condensed matter systems, from solutions to nanoconfined fluids to different kind of interfaces.

  7. A quantum-mechanics molecular-mechanics scheme for extended systems

    NASA Astrophysics Data System (ADS)

    Hunt, Diego; Sanchez, Veronica M.; Scherlis, Damián A.

    2016-08-01

    We introduce and discuss a hybrid quantum-mechanics molecular-mechanics (QM-MM) approach for Car–Parrinello DFT simulations with pseudopotentials and planewaves basis, designed for the treatment of periodic systems. In this implementation the MM atoms are considered as additional QM ions having fractional charges of either sign, which provides conceptual and computational simplicity by exploiting the machinery already existing in planewave codes to deal with electrostatics in periodic boundary conditions. With this strategy, both the QM and MM regions are contained in the same supercell, which determines the periodicity for the whole system. Thus, while this method is not meant to compete with non-periodic QM-MM schemes able to handle extremely large but finite MM regions, it is shown that for periodic systems of a few hundred atoms, our approach provides substantial savings in computational times by treating classically a fraction of the particles. The performance and accuracy of the method is assessed through the study of energetic, structural, and dynamical aspects of the water dimer and of the aqueous bulk phase. Finally, the QM-MM scheme is applied to the computation of the vibrational spectra of water layers adsorbed at the TiO2 anatase (1 0 1) solid–liquid interface. This investigation suggests that the inclusion of a second monolayer of H2O molecules is sufficient to induce on the first adsorbed layer, a vibrational dynamics similar to that taking place in the presence of an aqueous environment. The present QM-MM scheme appears as a very interesting tool to efficiently perform molecular dynamics simulations of complex condensed matter systems, from solutions to nanoconfined fluids to different kind of interfaces.

  8. A quantum-mechanics molecular-mechanics scheme for extended systems

    NASA Astrophysics Data System (ADS)

    Hunt, Diego; Sanchez, Veronica M.; Scherlis, Damián A.

    2016-08-01

    We introduce and discuss a hybrid quantum-mechanics molecular-mechanics (QM-MM) approach for Car-Parrinello DFT simulations with pseudopotentials and planewaves basis, designed for the treatment of periodic systems. In this implementation the MM atoms are considered as additional QM ions having fractional charges of either sign, which provides conceptual and computational simplicity by exploiting the machinery already existing in planewave codes to deal with electrostatics in periodic boundary conditions. With this strategy, both the QM and MM regions are contained in the same supercell, which determines the periodicity for the whole system. Thus, while this method is not meant to compete with non-periodic QM-MM schemes able to handle extremely large but finite MM regions, it is shown that for periodic systems of a few hundred atoms, our approach provides substantial savings in computational times by treating classically a fraction of the particles. The performance and accuracy of the method is assessed through the study of energetic, structural, and dynamical aspects of the water dimer and of the aqueous bulk phase. Finally, the QM-MM scheme is applied to the computation of the vibrational spectra of water layers adsorbed at the TiO2 anatase (1 0 1) solid-liquid interface. This investigation suggests that the inclusion of a second monolayer of H2O molecules is sufficient to induce on the first adsorbed layer, a vibrational dynamics similar to that taking place in the presence of an aqueous environment. The present QM-MM scheme appears as a very interesting tool to efficiently perform molecular dynamics simulations of complex condensed matter systems, from solutions to nanoconfined fluids to different kind of interfaces.

  9. A quantum-mechanics molecular-mechanics scheme for extended systems.

    PubMed

    Hunt, Diego; Sanchez, Veronica M; Scherlis, Damián A

    2016-08-24

    We introduce and discuss a hybrid quantum-mechanics molecular-mechanics (QM-MM) approach for Car-Parrinello DFT simulations with pseudopotentials and planewaves basis, designed for the treatment of periodic systems. In this implementation the MM atoms are considered as additional QM ions having fractional charges of either sign, which provides conceptual and computational simplicity by exploiting the machinery already existing in planewave codes to deal with electrostatics in periodic boundary conditions. With this strategy, both the QM and MM regions are contained in the same supercell, which determines the periodicity for the whole system. Thus, while this method is not meant to compete with non-periodic QM-MM schemes able to handle extremely large but finite MM regions, it is shown that for periodic systems of a few hundred atoms, our approach provides substantial savings in computational times by treating classically a fraction of the particles. The performance and accuracy of the method is assessed through the study of energetic, structural, and dynamical aspects of the water dimer and of the aqueous bulk phase. Finally, the QM-MM scheme is applied to the computation of the vibrational spectra of water layers adsorbed at the TiO2 anatase (1 0 1) solid-liquid interface. This investigation suggests that the inclusion of a second monolayer of H2O molecules is sufficient to induce on the first adsorbed layer, a vibrational dynamics similar to that taking place in the presence of an aqueous environment. The present QM-MM scheme appears as a very interesting tool to efficiently perform molecular dynamics simulations of complex condensed matter systems, from solutions to nanoconfined fluids to different kind of interfaces. PMID:27352028

  10. Quantum mechanics and experimental solid-state nuclear magnetic resonance analysis of strained molecular systems

    NASA Astrophysics Data System (ADS)

    Halling, Merrill David

    In this work 13C solid-state NMR and quantum mechanical studies of strained molecular systems are discussed. The chemical shift tensor values reported in this document were obtained using the FIREMAT method. Theoretical analyses of chemical shielding tensors were performed through the computer nodes operated by the Utah Center for High Performance Computing. Analyses were performed on sumanene, indenofluoranthene, tetrathiafulvalene, tetrathiafulvalene dimer, [2,2]paracyclophane, and 1,8-dioxa[8](2,7)pyrenophane. The FIREMAT data were fit using the TIGER data processing technique. TIGER provides a means to fit the FIREMAT data, accommodating its unique phase and relaxation characteristics. The details of the FIREMAT experiment are discussed in Chapter 1. The experimentally obtained chemical shift data were compared with calculated chemical shielding data. For these molecular systems, density functional theory was used along with the B3LYP exchange and correlation functionals. Multiple basis sets were used and relatively low errors are reported, between 2.0 ppm and 4.2 ppm. The errors reflect the difference between experimental and theoretical results. The relatively small errors are consistent with those of other polycyclic aromatic hydrocarbons (PAHs) and similar molecular systems. Chapter 2 discusses the three-dimensional aspect of tensor error analysis and how it is used in determining the errors associated with comparing two chemical shift tensors, i.e., theoretically derived and experimentally determined tensors. All error values reported and discussed in this dissertation are determined using this error analysis method. Molecular conformation may be explored by variation in chemical shift tensor principal values. The ring strain in curved polycyclic aromatic hydrocarbons can be associated with downfield shifts in the delta33 component of the chemical shift tensor. This is discussed in Chapters 3 and 5, as it relates to sumanene, indenofluoranthene, [2

  11. Quantum mechanics from invariance principles

    NASA Astrophysics Data System (ADS)

    Moldoveanu, Florin

    2015-07-01

    Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.

  12. Quantum mechanical streamlines. I - Square potential barrier

    NASA Technical Reports Server (NTRS)

    Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.

    1974-01-01

    Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.

  13. Supersymmetric Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    David, J.; Fernández, C.

    2010-10-01

    Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulae concerning SUSY QM of first second order for one-dimensional arbitrary systems, we will illustrate the method through the trigonometric Pöschl-Teller potentials. Some intrinsically related subjects, as the algebraic structure inherited by the new Hamiltonians and the corresponding coherent states will be analyzed. The technique will be as well implemented for periodic potentials, for which the corresponding spectrum is composed of allowed bands separated by energy gaps.

  14. Copenhagen quantum mechanics

    NASA Astrophysics Data System (ADS)

    Hollowood, Timothy J.

    2016-07-01

    In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950s development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrödinger cat states are the norm rather than curiosities generated in physicists' laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr's quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.

  15. Quantum mechanics, Furry's hypothesis, and a measure of decoherence in the K0K¯0 system

    NASA Astrophysics Data System (ADS)

    Bertlmann, R. A.; Grimus, W.; Hiesmayr, B. C.

    1999-12-01

    We consider strangeness correlations of the Einstein-Podolski-Rosen type in K0K¯0 pairs created in a JPC=1- state as a function of time under the hypothesis that spontaneous decoherence takes place. We parametrize the degree of decoherence by a factor (1-ζ) which multiplies the quantum-mechanical interference terms occurring in the amplitudes for like and unlike strangeness events and discuss the dependence of this procedure on the basis chosen in K0-K¯0 space to which the interference terms correspond. Consequently, all statements about the ``decoherence parameter'' ζ inferred from experimental data are basis dependent as well. We illustrate this point by estimating the value of ζ for the two bases \\{KL,KS\\} and \\{K0,K¯0\\} with the help of recent data of the CPLEAR experiment.

  16. Quantum mechanical NMR simulation algorithm for protein-size spin systems

    NASA Astrophysics Data System (ADS)

    Edwards, Luke J.; Savostyanov, D. V.; Welderufael, Z. T.; Lee, Donghan; Kuprov, Ilya

    2014-06-01

    Nuclear magnetic resonance spectroscopy is one of the few remaining areas of physical chemistry for which polynomially scaling quantum mechanical simulation methods have not so far been available. In this communication we adapt the restricted state space approximation to protein NMR spectroscopy and illustrate its performance by simulating common 2D and 3D liquid state NMR experiments (including accurate description of relaxation processes using Bloch-Redfield-Wangsness theory) on isotopically enriched human ubiquitin - a protein containing over a thousand nuclear spins forming an irregular polycyclic three-dimensional coupling lattice. The algorithm uses careful tailoring of the density operator space to only include nuclear spin states that are populated to a significant extent. The reduced state space is generated by analysing spin connectivity and decoherence properties: rapidly relaxing states as well as correlations between topologically remote spins are dropped from the basis set.

  17. Quantum Mechanics as Dualism

    NASA Astrophysics Data System (ADS)

    Jones, Robert

    2011-03-01

    I do not agree with mind-body dualism. Today the consensus view is that thought and mind is a combination of processes like memory, generalization, comparison, deduction, organization, induction, classification, feature detection, analogy, etc. performed by computational machinery. (R. Jones, Trans. of the Kansas Acad. Sci., vol. 109, # 3/4, 2006 and www.robert-w-jones.com, philosopher, theory of thought) But I believe that quantum mechanics is a more plausible dualist theory of reality. The quantum mechanical wave function is nonphysical, it exists in a 3N space (for an N body system) not in (x,y,z,t) 4-space, and does not possess physical properties. But real physical things like energy (which do exist in our 4-space world) influence the wave function and the wave function, in its turn, influences real physical things, like where a particle can be found in 4-space. The coupling between the spirit-like wave function and things found in the real (4-space) world (like energy) is via mathematical equations like the Schrodinger equation and Born normalization.

  18. Multiple environment single system quantum mechanical/molecular mechanical (MESS-QM/MM) calculations. 1. Estimation of polarization energies.

    PubMed

    Sodt, Alexander J; Mei, Ye; König, Gerhard; Tao, Peng; Steele, Ryan P; Brooks, Bernard R; Shao, Yihan

    2015-03-01

    In combined quantum mechanical/molecular mechanical (QM/MM) free energy calculations, it is often advantageous to have a frozen geometry for the quantum mechanical (QM) region. For such multiple-environment single-system (MESS) cases, two schemes are proposed here for estimating the polarization energy: the first scheme, termed MESS-E, involves a Roothaan step extrapolation of the self-consistent field (SCF) energy; whereas the other scheme, termed MESS-H, employs a Newton-Raphson correction using an approximate inverse electronic Hessian of the QM region (which is constructed only once). Both schemes are extremely efficient, because the expensive Fock updates and SCF iterations in standard QM/MM calculations are completely avoided at each configuration. They produce reasonably accurate QM/MM polarization energies: MESS-E can predict the polarization energy within 0.25 kcal/mol in terms of the mean signed error for two of our test cases, solvated methanol and solvated β-alanine, using the M06-2X or ωB97X-D functionals; MESS-H can reproduce the polarization energy within 0.2 kcal/mol for these two cases and for the oxyluciferin-luciferase complex, if the approximate inverse electronic Hessians are constructed with sufficient accuracy.

  19. Semiclassical anomalies of the quantum mechanical systems and their modifications for the asymptotic matching

    SciTech Connect

    Deniz, Coskun

    2011-08-15

    JWKB solutions to the Initial Value Problems (IVPs) of the Time Independent Schrodinger's Equation (TISE) for the Simple Linear Potentials (SLPs) with a turning point parameter have been studied according to the turning points by graphical analysis to test the results of the JWKB solutions and suggested modifications. The anomalies happening in the classically inaccessible region where the SLP function is smaller than zero and the results of the suggested modifications, which are in consistent with the quantum mechanical theories, to remove these anomalies in this region have been presented. The origins of the anomalies and verifications of the suggested modifications showing a great success in the results have also been studied in terms of a suggested M{sub ij}=S{sup {approx}}{sub i-1,j} matrix elements made up of the JWKB expansion terms, S{sub i-1,j} (where i = 1, 2, 3 and j 1, 2). The results of the modifications for the IVPs and their application to the Bound State Problems (BSPs) with an example application of the Harmonic Oscillator (HO) have been presented and their generalization for any potential function have been discussed and classified accordingly.

  20. PT quantum mechanics.

    PubMed

    Bender, Carl M; DeKieviet, Maarten; Klevansky, S P

    2013-04-28

    PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics.

  1. Facing quantum mechanical reality.

    PubMed

    Rohrlich, F

    1983-09-23

    Two recent precision experiments provide conclusive evidence against any local hidden variables theory and in favor of standard quantum mechanics. Therefore the epistemology and the ontology of quantum mechanics must now be taken more seriously than ever before. The consequences of the standard interpretation of quantum mechanics are summarized in nontechnical language. The implications of the finiteness of Planck's constant (h > 0) for the quantum world are as strange as the implications of the finiteness of the speed of light (c < infinity for space and time in relativity theory. Both lead to realities beyond our common experience that cannot be rejected.

  2. On the geometrization of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Tavernelli, Ivano

    2016-08-01

    Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave-particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie-Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space-time, as it is the case for gravitation in the general relativity.

  3. Scaling of volume to surface ratio and doubling time in growing unicellular organisms: Do cells appear quantum-mechanical systems?

    NASA Astrophysics Data System (ADS)

    Atanasov, Atanas Todorov

    2014-10-01

    The scaling of physical and biological characteristics of the living organisms is a basic method for searching of new biophysical laws. In series of previous studies the author showed that in Poikilotherms, Mammals and Aves, the volume to surface ratio V×S-1 (m) of organisms is proportional to their generation time Tgt(s) via growth rate v (m s-1): V×S-1 = vgr×Tr. The power and the correlation coefficients are near to 1.0. Aim of this study is: i) to prove with experimental data the validity of the above equation for Unicellular organisms and ii) to show that perhaps, the cells are quantum-mechanical systems. The data for body mass M (kg), density ρ (kg/m3), minimum and maximum doubling time Tdt (s) for 50 unicellular organisms are assembled from scientific sources, and the computer program `Statistics' is used for calculations. In result i) the analytical relationship from type: V×S-1 = 4.46ṡ10-11×Tdt was found, where vgr = 4.46×10-11 m/s and ii) it is shown that the products between cell mass M, cell length expressed by V/S ratio and growth rate vgr satisfied the Heisenberg uncertainty principle i.e. the inequalities V/S×M×vgr>h/2π and Tdt×M×vgr2>h/2π are valid, where h= 6.626×10-34 Jṡs is the Planck constant. This rise the question: do cells appear quantum-mechanical systems?

  4. Scaling of volume to surface ratio and doubling time in growing unicellular organisms: Do cells appear quantum-mechanical systems?

    SciTech Connect

    Atanasov, Atanas Todorov

    2014-10-06

    The scaling of physical and biological characteristics of the living organisms is a basic method for searching of new biophysical laws. In series of previous studies the author showed that in Poikilotherms, Mammals and Aves, the volume to surface ratio V×S{sup −1} (m) of organisms is proportional to their generation time T{sub gt}(s) via growth rate v (m s{sup −1}): V×S{sup −1} = v{sub gr}×T{sup r}. The power and the correlation coefficients are near to 1.0. Aim of this study is: i) to prove with experimental data the validity of the above equation for Unicellular organisms and ii) to show that perhaps, the cells are quantum-mechanical systems. The data for body mass M (kg), density ρ (kg/m{sup 3}), minimum and maximum doubling time T{sub dt} (s) for 50 unicellular organisms are assembled from scientific sources, and the computer program ‘Statistics’ is used for calculations. In result i) the analytical relationship from type: V×S{sup −1} = 4.46⋅10{sup −11}×T{sub dt} was found, where v{sub gr} = 4.46×10{sup −11} m/s and ii) it is shown that the products between cell mass M, cell length expressed by V/S ratio and growth rate v{sub gr} satisfied the Heisenberg uncertainty principle i.e. the inequalities V/S×M×v{sub gr}>h/2π and T{sub dt}×M×v{sub gr}{sup 2}>h/2π are valid, where h= 6.626×10{sup −34} J⋅s is the Planck constant. This rise the question: do cells appear quantum-mechanical systems?.

  5. Supersymmetry in quantum mechanics

    SciTech Connect

    Khare, Avinash

    2004-12-23

    An elementary introduction is given to the subject of supersymmetry in quantum mechanics which can be understood and appreciated by any one who has taken a first course in quantum mechanics. We demonstrate with explicit examples that given a solvable problem in quantum mechanics with n bound states, one can construct n new exactly solvable Hamiltonians having n - 1, n - 2,..., 0 bound states. The relationship between the eigenvalues, eigenfunctions and scattering matrix of the supersymmetric partner potentials is derived and a class of reflectionless potentials are explicitly constructed. We extend the operator method of solving the one-dimensional harmonic oscillator problem to a class of potentials called shape-invariant potentials. It is worth emphasizing that this class includes almost all the solvable problems that are found in the standard text books on quantum mechanics. Further, we show that given any potential with at least one bound state, one can very easily construct one continuous parameter family of potentials having same eigenvalues and s-matrix. The supersymmetry inspired WKB approximation (SWKB) is also discussed and it is shown that unlike the usual WKB, the lowest order SWKB approximation is exact for the shape-invariant potentials and further, this approximation is not only exact for large quantum numbers but by construction, it is also exact for the ground state. Finally, we also construct new exactly solvable periodic potentials by using the machinery of supersymmetric quantum mechanics.

  6. Lagrangians and Systems They Describe-How Not to Treat Dissipation in Quantum Mechanics.

    ERIC Educational Resources Information Center

    Ray, John R.

    1979-01-01

    The author argues that a Lagrangian that yields equations of motion for a damped simple harmonic oscillator does not describe this system, but a completely different physical system, and constructs a physical system that the Lagrangian describes and derives some of its properties. (Author/GA)

  7. Grassmann matrix quantum mechanics

    DOE PAGES

    Anninos, Dionysios; Denef, Frederik; Monten, Ruben

    2016-04-21

    We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kähler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit.more » In conclusion, we discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.« less

  8. An eight-dimensional quantum mechanical Hamiltonian for X + YCZ3 system and its applications to H + CH4 reaction

    NASA Astrophysics Data System (ADS)

    Liu, Rui; Xiong, Hongwei; Yang, Minghui

    2012-11-01

    An eight-dimensional quantum mechanical Hamiltonian has been proposed based on Palma and Clary's model in which the non-reacting CZ3 group keeps a C3v symmetry in the X + YCZ3 ↔ XY + CZ3 reaction J. Palma and D. C. Clary [J. Chem. Phys. 112, 1859 (2000), 10.1063/1.480749]. By transforming the original Cartesian coordinate system (x, s) into a scaled polar coordinate system (q, γ), the vibrational Hamiltonian of CZ3 group is expressed in a simple form with a clear physical picture. This Hamiltonian is used to investigate the H + CH4 → H2 + CH3 reaction on the Jordan-Gilbert potential energy surface. The total reaction probabilities are calculated for the initial ground state, and umbrella, bending, symmetric, and asymmetric stretching excited states of CH4 with total angular momentum J = 0. The integral cross sections for the reaction are also studied for these initial vibrational states with a centrifugal-sudden approximation. The total integral cross sections for the asymmetric stretching vibrational excited state are in good agreement with the experimental observations. The results also showed the difference of dynamical behavior between reactions from symmetric and asymmetric stretching excited states. The thermal rate constants are calculated for the temperature range T = 250-2000 K and compared with the experimental and other theoretical results.

  9. Superiority of semiclassical over quantum mechanical calculations for a three-dimensional system

    NASA Astrophysics Data System (ADS)

    Main, Jörg; Wunner, Günter; Atılgan, Erdinç; Taylor, Howard S.; Dando, Paul A.

    2002-12-01

    In systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods. However, this situation can be reversed with increasing dimension of the problem. For a three-dimensional system, viz. the hyperbolic four-sphere scattering system, we demonstrate the superiority of semiclassical versus quantum calculations. Semiclassical resonances can easily be obtained even in energy regions which are unattainable with the currently available quantum techniques.

  10. Time-dependent perturbation of a two-state quantum mechanical system

    NASA Technical Reports Server (NTRS)

    Dion, D. R.

    1974-01-01

    A two- (nondegenerate) level quantum system interacting with a classical monochromatic radiation field is described. The existing work on this problem is reviewed and some novel aspects of the problems are presented.

  11. Ergodicity breaking and wave-function statistics in disordered interacting systems

    SciTech Connect

    De Luca, Andrea

    2014-08-20

    We present the study of the structure of many-body eigenfunctions in a one-dimensional disordered spin chain. We discuss the choice of an appropriate basis in the Hilbert space, where the problem can be seen as an Anderson model defined on a high-dimensional non-trivial graph, determined by the many-body Hamiltonian. The comparison with the usual behavior of wave-functions in finite dimensional Anderson localization allows us to put in light the main differences of the many-body case. At high disorder, the typical eigenfunctions do not seem to localize though they occupy a infinitesimal portion of the Hilbert space in the thermodynamic limit. We perform a detailed analysis of the distribution of the wave-function coefficients and their peculiar scaling in the small and large disorder phase. We propose a criterion to identify the position of the transition by looking at the long tails of these distributions. The results coming from exact diagonalization show signs of breaking of ergodicity when the disorder reaches a critical value that agrees with the estimation of the many-body localization transition in the same model.

  12. A bosonized formulation of the supersymmetric quantum mechanics for shape-invariant potential systems

    NASA Astrophysics Data System (ADS)

    Aleixo, A. N. F.; Balantekin, A. B.

    2014-08-01

    We consider the minimal bosonization realization of supersymmetric shape-invariant systems where generalized supercharge operators are constructed using the partner supersymmetric operators, the parameter potential translation formalism and the reflection operator. We obtain the solution of the eigenvalue equation and study the quantum dynamics of the supersymmetric system including terms in the Hamiltonian which are constructed using the combination of the bosonized supercharge operators. The connections between the bosonized supersymmetric formalism, the Bose-Fermi transformation and the generalization of the R-deformed Heisenberg algebra are discussed. As an illustration, we apply the generalized formalism for the case of the trigonometric Rosen-Morse potential.

  13. Optimization of a relativistic quantum mechanical engine.

    PubMed

    Peña, Francisco J; Ferré, Michel; Orellana, P A; Rojas, René G; Vargas, P

    2016-08-01

    We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two noninteracting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power.

  14. Optimization of a relativistic quantum mechanical engine

    NASA Astrophysics Data System (ADS)

    Peña, Francisco J.; Ferré, Michel; Orellana, P. A.; Rojas, René G.; Vargas, P.

    2016-08-01

    We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two noninteracting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power.

  15. Optimization of a relativistic quantum mechanical engine.

    PubMed

    Peña, Francisco J; Ferré, Michel; Orellana, P A; Rojas, René G; Vargas, P

    2016-08-01

    We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two noninteracting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power. PMID:27627248

  16. Quantum mechanical theory of a structured atom-diatom collision system - A + BC/1-Sigma/

    NASA Technical Reports Server (NTRS)

    Devries, P. L.; George, T. F.

    1977-01-01

    The problem of a 2-p state atom colliding with a singlet sigma state diatom, which involves multiple potential surfaces, is investigated. Within a diabatic representation for the electronic degrees of freedom (plus spin-orbit interaction), coupled scattering equations are derived in both space-fixed and body-fixed coordinate systems. Coefficients, analogous to Percival-Seaton coefficients, are obtained. Approximations to the exact equations, including angular momenta decoupling approximations, are discussed for both the space-fixed and body-fixed formalisms.

  17. Real-time transport in open quantum systems from PT-symmetric quantum mechanics

    NASA Astrophysics Data System (ADS)

    Elenewski, Justin E.; Chen, Hanning

    2014-08-01

    Nanoscale electronic transport is of intense technological interest, with applications ranging from semiconducting devices and molecular junctions to charge migration in biological systems. Most explicit theoretical approaches treat transport using a combination of density functional theory (DFT) and nonequilibrium Green's functions. This is a static formalism, with dynamic response properties accommodated only through complicated extensions. To circumvent this limitation, the carrier density may be propagated using real-time time-dependent DFT (RT-TDDFT), with boundary conditions corresponding to an open quantum system. Complex absorbing potentials can emulate outgoing particles at the simulation boundary, although these do not account for introduction of charge density. It is demonstrated that the desired positive particle flux is afforded by a class of PT-symmetric generating potentials that are characterized by anisotropic transmission resonances. These potentials add density every time a particle traverses the cell boundary, and may be used to engineer a continuous pulse train for incident packets. This is a first step toward developing a complete transport formalism unique to RT-TDDFT.

  18. The new physician as unwitting quantum mechanic: is adapting Dirac's inference system best practice for personalized medicine, genomics, and proteomics?

    PubMed

    Robson, Barry

    2007-08-01

    What is the Best Practice for automated inference in Medical Decision Support for personalized medicine? A known system already exists as Dirac's inference system from quantum mechanics (QM) using bra-kets and bras where A and B are states, events, or measurements representing, say, clinical and biomedical rules. Dirac's system should theoretically be the universal best practice for all inference, though QM is notorious as sometimes leading to bizarre conclusions that appear not to be applicable to the macroscopic world of everyday world human experience and medical practice. It is here argued that this apparent difficulty vanishes if QM is assigned one new multiplication function @, which conserves conditionality appropriately, making QM applicable to classical inference including a quantitative form of the predicate calculus. An alternative interpretation with the same consequences is if every i = radical-1 in Dirac's QM is replaced by h, an entity distinct from 1 and i and arguably a hidden root of 1 such that h2 = 1. With that exception, this paper is thus primarily a review of the application of Dirac's system, by application of linear algebra in the complex domain to help manipulate information about associations and ontology in complicated data. Any combined bra-ket can be shown to be composed only of the sum of QM-like bra and ket weights c(), times an exponential function of Fano's mutual information measure I(A; B) about the association between A and B, that is, an association rule from data mining. With the weights and Fano measure re-expressed as expectations on finite data using Riemann's Incomplete (i.e., Generalized) Zeta Functions, actual counts of observations for real world sparse data can be readily utilized. Finally, the paper compares identical character, distinguishability of states events or measurements, correlation, mutual information, and orthogonal character, important issues in data mining

  19. The new physician as unwitting quantum mechanic: is adapting Dirac's inference system best practice for personalized medicine, genomics, and proteomics?

    PubMed

    Robson, Barry

    2007-08-01

    What is the Best Practice for automated inference in Medical Decision Support for personalized medicine? A known system already exists as Dirac's inference system from quantum mechanics (QM) using bra-kets and bras where A and B are states, events, or measurements representing, say, clinical and biomedical rules. Dirac's system should theoretically be the universal best practice for all inference, though QM is notorious as sometimes leading to bizarre conclusions that appear not to be applicable to the macroscopic world of everyday world human experience and medical practice. It is here argued that this apparent difficulty vanishes if QM is assigned one new multiplication function @, which conserves conditionality appropriately, making QM applicable to classical inference including a quantitative form of the predicate calculus. An alternative interpretation with the same consequences is if every i = radical-1 in Dirac's QM is replaced by h, an entity distinct from 1 and i and arguably a hidden root of 1 such that h2 = 1. With that exception, this paper is thus primarily a review of the application of Dirac's system, by application of linear algebra in the complex domain to help manipulate information about associations and ontology in complicated data. Any combined bra-ket can be shown to be composed only of the sum of QM-like bra and ket weights c(), times an exponential function of Fano's mutual information measure I(A; B) about the association between A and B, that is, an association rule from data mining. With the weights and Fano measure re-expressed as expectations on finite data using Riemann's Incomplete (i.e., Generalized) Zeta Functions, actual counts of observations for real world sparse data can be readily utilized. Finally, the paper compares identical character, distinguishability of states events or measurements, correlation, mutual information, and orthogonal character, important issues in data mining

  20. Principles of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Landé, Alfred

    2013-10-01

    ödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantum mechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantum mechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.

  1. Is Q for Quantum? From Quantum Mechanics to Formation of the Solar System

    NASA Technical Reports Server (NTRS)

    Wilson, T. L.; Mittlefehldt, D. W.

    2006-01-01

    The realization in 1985 that fullerenes exist in nature [1] as a third form of carbon-carbon clustering, continues to inspire new areas of research. In particular, the study of closed-cage endohedral fullerenes [2-6] is of scientific interest because of its potential application in a number of promising fields from medical imaging to astrophysics. One of these is to provide a possible chronometer for studying the age and origin of certain astromaterials in the solar system. Fullerenes are closed carbon cages that are fundamentally related to a long-standing debate over the "Q-Phase" origin of planetary noble gases in carbonaceous chondrites [7]. Although Q-phase has been identified as the carrier of planetary noble gases [8- 10], its physical nature has not been explained. Our limited understanding of it is based primarily on the laboratory chemical processing which it survives as well as the fact that it must have been widely distributed in the solar nebula [11]. Yet as important as it might be while preoccupying some 30 years of research, the question of what actually is Q-phase remains unresolved.

  2. Hybrid Quantum Mechanics/Molecular Mechanics/Coarse Grained Modeling: A Triple-Resolution Approach for Biomolecular Systems.

    PubMed

    Sokkar, Pandian; Boulanger, Eliot; Thiel, Walter; Sanchez-Garcia, Elsa

    2015-04-14

    We present a hybrid quantum mechanics/molecular mechanics/coarse-grained (QM/MM/CG) multiresolution approach for solvated biomolecular systems. The chemically important active-site region is treated at the QM level. The biomolecular environment is described by an atomistic MM force field, and the solvent is modeled with the CG Martini force field using standard or polarizable (pol-CG) water. Interactions within the QM, MM, and CG regions, and between the QM and MM regions, are treated in the usual manner, whereas the CG-MM and CG-QM interactions are evaluated using the virtual sites approach. The accuracy and efficiency of our implementation is tested for two enzymes, chorismate mutase (CM) and p-hydroxybenzoate hydroxylase (PHBH). In CM, the QM/MM/CG potential energy scans along the reaction coordinate yield reaction energies that are too large, both for the standard and polarizable Martini CG water models, which can be attributed to adverse effects of using large CG water beads. The inclusion of an atomistic MM water layer (10 Å for uncharged CG water and 5 Å for polarizable CG water) around the QM region improves the energy profiles compared to the reference QM/MM calculations. In analogous QM/MM/CG calculations on PHBH, the use of the pol-CG description for the outer water does not affect the stabilization of the highly charged FADHOOH-pOHB transition state compared to the fully atomistic QM/MM calculations. Detailed performance analysis in a glycine-water model system indicates that computation times for QM energy and gradient evaluations at the density functional level are typically reduced by 40-70% for QM/MM/CG relative to fully atomistic QM/MM calculations.

  3. Emergence of quantum mechanics from a sub-quantum statistical mechanics

    NASA Astrophysics Data System (ADS)

    Grössing, Gerhard

    2014-07-01

    A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level. It is further demonstrated both analytically and with the aid of computer simulations that our model provides explanations for various quantum effects such as double-slit or n-slit interference. We show the averaged trajectories emerging from our model to be identical to Bohmian trajectories, albeit without the need to invoke complex wavefunctions or any other quantum mechanical tool. Finally, the model provides new insights into the origins of entanglement, and, in particular, into the phenomenon of a "systemic" non-locality.

  4. Quantum Mechanics From the Cradle?

    ERIC Educational Resources Information Center

    Martin, John L.

    1974-01-01

    States that the major problem in learning quantum mechanics is often the student's ignorance of classical mechanics and that one conceptual hurdle in quantum mechanics is its statistical nature, in contrast to the determinism of classical mechanics. (MLH)

  5. Epigenetics: Biology's Quantum Mechanics.

    PubMed

    Jorgensen, Richard A

    2011-01-01

    The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene - the molecular biological view and the epigenetic view - are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider.

  6. Epigenetics: Biology's Quantum Mechanics.

    PubMed

    Jorgensen, Richard A

    2011-01-01

    The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene - the molecular biological view and the epigenetic view - are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider. PMID:22639577

  7. Quantum Mechanics, Volume 1

    NASA Astrophysics Data System (ADS)

    Cohen-Tannoudji, Claude; Diu, Bernard; Laloe, Frank

    1986-06-01

    Beginning students of quantum mechanics frequently experience difficulties separating essential underlying principles from the specific examples to which these principles have been historically applied. Nobel-Prize-winner Claude Cohen-Tannoudji and his colleagues have written this book to eliminate precisely these difficulties. Fourteen chapters provide a clarity of organization, careful attention to pedagogical details, and a wealth of topics and examples which make this work a textbook as well as a timeless reference, allowing to tailor courses to meet students' specific needs. Each chapter starts with a clear exposition of the problem which is then treated, and logically develops the physical and mathematical concept. These chapters emphasize the underlying principles of the material, undiluted by extensive references to applications and practical examples which are put into complementary sections. The book begins with a qualitative introduction to quantum mechanical ideas using simple optical analogies and continues with a systematic and thorough presentation of the mathematical tools and postulates of quantum mechanics as well as a discussion of their physical content. Applications follow, starting with the simplest ones like e.g. the harmonic oscillator, and becoming gradually more complicated (the hydrogen atom, approximation methods, etc.). The complementary sections each expand this basic knowledge, supplying a wide range of applications and related topics as well as detailed expositions of a large number of special problems and more advanced topics, integrated as an essential portion of the text.

  8. Feynman's simple quantum mechanics

    NASA Astrophysics Data System (ADS)

    Taylor, Edwin F.

    1997-03-01

    This sample class presents an alternative to the conventional introduction to quantum mechanics and describes its current use in a credit course. This alternative introduction rests on theory presented in professional and popular writings by Richard Feynman. Feynman showed that Nature gives a simple command to the electron: "Explore all paths." All of nonrelativistic quantum mechanics, among other fundamental results, comes from this command. With a desktop computer the student points and clicks to tell a modeled electron which paths to follow. The computer then shows the results, which embody the elemental strangeness and paradoxical behaviors of the world of the very small. Feynman's approach requires few equations and provides a largely non-mathematical introduction to the wave function of conventional quantum mechanics. Draft software and materials already used for two semesters in an e-mail computer conference credit university course show that Feynman's approach works well with a variety of students. The sample class explores computer and written material and describes the next steps in its development.

  9. On a quantum mechanical system theory of the origin of life: from the Stapp-model to the origin of natural symbols

    NASA Astrophysics Data System (ADS)

    Balázs, András

    2016-01-01

    The Heisenberg-James-Stapp (quantum mechanical) mind model is surveyed and criticized briefly. The criticism points out that the model, while being essentially consistent concerning (human) consciousness, fundamentally lacks the evolutional point of view both onto- and phylogenetically. Ethology and other than Jamesian psychology is quoted and a quantum mechanical theoretical scheme is suggested to essentially extend Stapp's frame in an evolutionary context. It is proposed that its central supposition, spontaneous quantum measurement can be better utilized in an investigation of the origin of the "subjective" process, having come about concomitantly with the chemistry of the origin of life. We dwell on its applicability at this latter process, at its heart standing, it is supposed, the endophysical nonlinear "self-measurement" of (quantum mechanically describable) matter, and so our investigation is extended to this primeval phenomenon. It is suggested that the life phenomenon is an indirect C* → (W*) → C* quantum algebraic process transition, where the (W*) system would represent the living state. Summarized also are our previous results on an internalized, "reversed", time process, introduced originally by Gunji, which is subordinated to the external "forwards" time evolution, driving towards symmetry by gradual space-mappings, where the original splitting-up must have come about in a spontaneous symmetry breaking nonlinear "self-measurement" of matter in an endophysical World.

  10. Quantum mechanics of black holes.

    PubMed

    Witten, Edward

    2012-08-01

    The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.

  11. Quantum mechanics of black holes.

    PubMed

    Witten, Edward

    2012-08-01

    The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely. PMID:22859480

  12. Quantum mechanics without state vectors

    NASA Astrophysics Data System (ADS)

    Weinberg, Steven

    2014-10-01

    Because the state vectors of isolated systems can be changed in entangled states by processes in other isolated systems, keeping only the density matrix fixed, it is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying only on density matrices. The density matrix is defined here by the formula giving the mean values of physical quantities, which implies the same properties as the usual definition in terms of state vectors and their probabilities. This change in the description of physical states opens up a large variety of new ways that the density matrix may transform under various symmetries, different from the unitary transformations of ordinary quantum mechanics. Such new transformation properties have been explored before, but so far only for the symmetry of time translations into the future, treated as a semigroup. Here, new transformation properties are studied for general symmetry transformations forming groups, not just semigroups. Arguments that such symmetries should act on the density matrix as in ordinary quantum mechanics are presented, but all of these arguments are found to be inconclusive.

  13. Causal structure in categorical quantum mechanics

    NASA Astrophysics Data System (ADS)

    Lal, Raymond Ashwin

    Categorical quantum mechanics is a way of formalising the structural features of quantum theory using category theory. It uses compound systems as the primitive notion, which is formalised by using symmetric monoidal categories. This leads to an elegant formalism for describing quantum protocols such as quantum teleportation. In particular, categorical quantum mechanics provides a graphical calculus that exposes the information flow of such protocols in an intuitive way. However, the graphical calculus also reveals surprising features of these protocols; for example, in the quantum teleportation protocol, information appears to flow `backwards-in-time'. This leads to question of how causal structure can be described within categorical quantum mechanics, and how this might lead to insight regarding the structural compatibility between quantum theory and relativity. This thesis is concerned with the project of formalising causal structure in categorical quantum mechanics. We begin by studying an abstract view of Bell-type experiments, as described by `no-signalling boxes', and we show that under time-reversal no-signalling boxes generically become signalling. This conflicts with the underlying symmetry of relativistic causal structure. This leads us to consider the framework of categorical quantum mechanics from the perspective of relativistic causal structure. We derive the properties that a symmetric monoidal category must satisfy in order to describe systems in such a background causal structure. We use these properties to define a new type of category, and this provides a formal framework for describing protocols in spacetime. We explore this new structure, showing how it leads to an understanding of the counter-intuitive information flow of protocols in categorical quantum mechanics. We then find that the formal properties of our new structure are naturally related to axioms for reconstructing quantum theory, and we show how a reconstruction scheme based on

  14. A signed particle formulation of non-relativistic quantum mechanics

    SciTech Connect

    Sellier, Jean Michel

    2015-09-15

    A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schrödinger time-dependent wave-function. Its classical limit is discussed and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the validity of the suggested approach.

  15. Consecutive Measurements in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Glick, Jennifer R.; Adami, Christoph

    The physics of quantum measurement still continues to puzzle with no resolution in sight between competing interpretations, in particular because no interpretation has so far produced predictions that would be falsifiable via experiment. Here we present an analysis of consecutive projective measurements performed on a quantum state using quantum information theory, where the entanglement between the quantum system and a measuring device is explicitly taken into account, and where the consecutive measurements increase the joint Hilbert space while the wavefunction of the joint system never collapses. Using this relative-state formalism we rederive well-known results for the pairwise correlation between any two measurement devices, but show that considering the joint as well as conditional entropy of three devices reveals a difference between the collapse and no-collapse pictures of quantum measurement that is experimentally testable. This research was funded by a Michigan State University Enrichment Fellowship.

  16. Quantum mechanical embedding theory based on a unique embedding potential

    SciTech Connect

    Chen Huang; Pavone, Michele; Carter, Emily A.

    2011-04-21

    We remove the nonuniqueness of the embedding potential that exists in most previous quantum mechanical embedding schemes by letting the environment and embedded region share a common embedding (interaction) potential. To efficiently solve for the embedding potential, an optimized effective potential method is derived. This embedding potential, which eschews use of approximate kinetic energy density functionals, is then used to describe the environment while a correlated wavefunction (CW) treatment of the embedded region is employed. We first demonstrate the accuracy of this new embedded CW (ECW) method by calculating the van der Waals binding energy curve between a hydrogen molecule and a hydrogen chain. We then examine the prototypical adsorption of CO on a metal surface, here the Cu(111) surface. In addition to obtaining proper site ordering (top site most stable) and binding energies within this theory, the ECW exhibits dramatic changes in the p-character of the CO 4{sigma} and 5{sigma} orbitals upon adsorption that agree very well with x-ray emission spectra, providing further validation of the theory. Finally, we generalize our embedding theory to spin-polarized quantum systems and discuss the connection between our theory and partition density functional theory.

  17. Use of Nonequilibrium Work Methods to Compute Free Energy Differences Between Molecular Mechanical and Quantum Mechanical Representations of Molecular Systems.

    PubMed

    Hudson, Phillip S; Woodcock, H Lee; Boresch, Stefan

    2015-12-01

    Carrying out free energy simulations (FES) using quantum mechanical (QM) Hamiltonians remains an attractive, albeit elusive goal. Renewed efforts in this area have focused on using "indirect" thermodynamic cycles to connect "low level" simulation results to "high level" free energies. The main obstacle to computing converged free energy results between molecular mechanical (MM) and QM (ΔA(MM→QM)), as recently demonstrated by us and others, is differences in the so-called "stiff" degrees of freedom (e.g., bond stretching) between the respective energy surfaces. Herein, we demonstrate that this problem can be efficiently circumvented using nonequilibrium work (NEW) techniques, i.e., Jarzynski's and Crooks' equations. Initial applications of computing ΔA(NEW)(MM→QM), for blocked amino acids alanine and serine as well as to generate butane's potentials of mean force via the indirect QM/MM FES method, showed marked improvement over traditional FES approaches. PMID:26539729

  18. Use of Nonequilibrium Work Methods to Compute Free Energy Differences Between Molecular Mechanical and Quantum Mechanical Representations of Molecular Systems.

    PubMed

    Hudson, Phillip S; Woodcock, H Lee; Boresch, Stefan

    2015-12-01

    Carrying out free energy simulations (FES) using quantum mechanical (QM) Hamiltonians remains an attractive, albeit elusive goal. Renewed efforts in this area have focused on using "indirect" thermodynamic cycles to connect "low level" simulation results to "high level" free energies. The main obstacle to computing converged free energy results between molecular mechanical (MM) and QM (ΔA(MM→QM)), as recently demonstrated by us and others, is differences in the so-called "stiff" degrees of freedom (e.g., bond stretching) between the respective energy surfaces. Herein, we demonstrate that this problem can be efficiently circumvented using nonequilibrium work (NEW) techniques, i.e., Jarzynski's and Crooks' equations. Initial applications of computing ΔA(NEW)(MM→QM), for blocked amino acids alanine and serine as well as to generate butane's potentials of mean force via the indirect QM/MM FES method, showed marked improvement over traditional FES approaches.

  19. Superstrings and the Foundations of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    't Hooft, Gerard

    2014-05-01

    It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are usually categorically rejected, because of Bell's powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions.

  20. Polymer quantum mechanics and its continuum limit

    SciTech Connect

    Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A.

    2007-08-15

    A rather nonstandard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model.

  1. Probability Interpretation of Quantum Mechanics.

    ERIC Educational Resources Information Center

    Newton, Roger G.

    1980-01-01

    This paper draws attention to the frequency meaning of the probability concept and its implications for quantum mechanics. It emphasizes that the very meaning of probability implies the ensemble interpretation of both pure and mixed states. As a result some of the "paradoxical" aspects of quantum mechanics lose their counterintuitive character.…

  2. Quantum mechanics over sets

    NASA Astrophysics Data System (ADS)

    Ellerman, David

    2014-03-01

    In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantum mechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.

  3. Propagators in polymer quantum mechanics

    SciTech Connect

    Flores-González, Ernesto Morales-Técotl, Hugo A. Reyes, Juan D.

    2013-09-15

    Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has been used to represent some aspects of the loop quantization in a simpler context, and, on the other, it has been applied to each of the infinite mechanical modes of other systems. Indeed, this polymer approach was recently implemented for the free scalar field propagator. In this work we compute the polymer propagators of the free particle and a particle in a box; amusingly, just as in the non polymeric case, the one of the particle in a box may be computed also from that of the free particle using the method of images. We verify the propagators hereby obtained satisfy standard properties such as: consistency with initial conditions, composition and Green’s function character. Furthermore they are also shown to reduce to the usual Schrödinger propagators in the limit of small parameter μ{sub 0}, the length scale introduced in the polymer dynamics and which plays a role analog of that of Planck length in Quantum Gravity. -- Highlights: •Formulas for propagators of free and particle in a box in polymer quantum mechanics. •Initial conditions, composition and Green’s function character is checked. •Propagators reduce to corresponding Schrödinger ones in an appropriately defined limit. •Results show overall consistency of the polymer framework. •For the particle in a box results are also verified using formula from method of images.

  4. Perturbation Theory for Quantum Mechanics in its Hessenberg-Matrix Representation

    NASA Astrophysics Data System (ADS)

    Znojil, Miloslav

    For years, the partial integrability in quantum mechanics [e.g., the exceptional terminating Lanczos solutions or the so called quasi-exactly solvable "next-to-elementary" systems] represented a challenge in perturbation theory. The main difficulty lied in an incompleteness of the available zero-order wavefunctions and in the related impossibility of an easy construction of the necessary zero-order propagators. We describe a solution of this problem, based on an unusual choice of model space. A few examples illustrate the underlying technicalities: Paying detailed attention to the Hessenberg-matrix Hamiltonians, our formalism compensates the incompleteness of integrability by a slightly less elementary (viz., non-diagonal but still triangular) matrix structure of its propagators.

  5. Gaussian effective potential: Quantum mechanics

    NASA Astrophysics Data System (ADS)

    Stevenson, P. M.

    1984-10-01

    We advertise the virtues of the Gaussian effective potential (GEP) as a guide to the behavior of quantum field theories. Much superior to the usual one-loop effective potential, the GEP is a natural extension of intuitive notions familiar from quantum mechanics. A variety of quantum-mechanical examples are studied here, with an eye to field-theoretic analogies. Quantum restoration of symmetry, dynamical mass generation, and "quantum-mechanical resuscitation" are among the phenomena discussed. We suggest how the GEP could become the basis of a systematic approximation procedure. A companion paper will deal with scalar field theory.

  6. Quantum mechanical resonance calculations using an energy selected basis in hyperspherical coordinates

    NASA Astrophysics Data System (ADS)

    Montgomery, Jason

    2007-12-01

    Scattering resonances play a key role in many chemical processes, including unimolecular and bimolecular reactions and photodissociation. A significant theoretical emphasis over the past several decades has been placed on accurate resonance calculations for polyatomic systems. In spite of such efforts, a quantum treatment of molecular systems which exhibit a high density of states and strong coordinate coupling near dissociation remains a formidable task. The research described herein employs improved quantum mechanical methods to calculate a representation of nuclear motion, both bound and unbound, which is used subsequently to calculate accurate resonance energies and lifetimes for two triatomic systems: the neon trimer and ozone. Specifically, theory and results are given regarding the construction of an optimal, L2 eigenbasis using techniques such as the discrete variable representation, the energy selected basis (ESB) method, and iterative diagonalization methods. A new energy selection method is also developed and implemented for the neon trimer. Subsequent resonance calculations are described which make use of the artificial boundary inhomogeneity (ABI) method, adapted to work with the above mentioned ESB and hyperspherical coordinates. The ABI method is used to calculate a set of linearly independent wavefunctions (LIWs) at a given energy for the representation of the scattering wavefunction. Resonance parameters are obtained by imposing scattering boundary conditions on a linear combination of LIWs and solving for the S-matrix, S, its energy derivative, dS/dE, and the Smith lifetime matrix, Q. When available, comparisons are made with previously reported calculations.

  7. A coefficient average approximation towards Gutzwiller wavefunction formalism

    NASA Astrophysics Data System (ADS)

    Liu, Jun; Yao, Yongxin; Wang, Cai-Zhuang; Ho, Kai-Ming

    2015-06-01

    Gutzwiller wavefunction is a physically well-motivated trial wavefunction for describing correlated electron systems. In this work, a new approximation is introduced to facilitate the evaluation of the expectation value of any operator within the Gutzwiller wavefunction formalism. The basic idea is to make use of a specially designed average over Gutzwiller wavefunction coefficients expanded in the many-body Fock space to approximate the ratio of expectation values between a Gutzwiller wavefunction and its underlying noninteracting wavefunction. To check with the standard Gutzwiller approximation (GA), we test its performance on single band systems and find quite interesting properties. On finite systems, we noticed that it gives superior performance over GA, while on infinite systems it asymptotically approaches GA. Analytic analysis together with numerical tests are provided to support this claimed asymptotical behavior. Finally, possible improvements on the approximation and its generalization towards multiband systems are illustrated and discussed.

  8. A coefficient average approximation towards Gutzwiller wavefunction formalism.

    PubMed

    Liu, Jun; Yao, Yongxin; Wang, Cai-Zhuang; Ho, Kai-Ming

    2015-06-24

    Gutzwiller wavefunction is a physically well-motivated trial wavefunction for describing correlated electron systems. In this work, a new approximation is introduced to facilitate the evaluation of the expectation value of any operator within the Gutzwiller wavefunction formalism. The basic idea is to make use of a specially designed average over Gutzwiller wavefunction coefficients expanded in the many-body Fock space to approximate the ratio of expectation values between a Gutzwiller wavefunction and its underlying noninteracting wavefunction. To check with the standard Gutzwiller approximation (GA), we test its performance on single band systems and find quite interesting properties. On finite systems, we noticed that it gives superior performance over GA, while on infinite systems it asymptotically approaches GA. Analytic analysis together with numerical tests are provided to support this claimed asymptotical behavior. Finally, possible improvements on the approximation and its generalization towards multiband systems are illustrated and discussed.

  9. Dissipative Forces and Quantum Mechanics

    ERIC Educational Resources Information Center

    Eck, John S.; Thompson, W. J.

    1977-01-01

    Shows how to include the dissipative forces of classical mechanics in quantum mechanics by the use of non-Hermetian Hamiltonians. The Ehrenfest theorem for such Hamiltonians is derived, and simple examples which show the classical correspondences are given. (MLH)

  10. Calculation of the electron two slit experiment using a quantum mechanical variational principle

    SciTech Connect

    Harrison, Alan K.

    2012-04-17

    A nonlocal relativistic variational principle (VP) has recently been proposed as an alternative to the Dirac wave equation of standard quantum mechanics. We apply that principle to the electron two-slit experiment. The detection system is modelled as a screen made of atoms, any one of which can be excited by the incident electron, but we avoid restricting the detection mechanism further. The VP is shown to predict that, at the time the electron reaches the screen, its wavefunction will be localized to the neighborhood of a single atom, resulting in a position-type measurement. In an ensemble of such experiments ('identically prepared' except that the initial phase of the wavefunction - the hidden variable in the VP formulation - is sampled over the expected uniform distribution), the distribution of measured positions will reproduce the interference pattern predicted by the Dirac equation. We also demonstrate that with a detection system designed fundamentally to detect the electron's transverse wavelength rather than its position, the VP predicts that one such mode will be detected, that is, a wavelength measurement will result. Finally, it is shown that these results are unchanged in the 'delayed choice' variant of the experiment.

  11. Theoretical modeling of large molecular systems. Advances in the local self consistent field method for mixed quantum mechanics/molecular mechanics calculations.

    PubMed

    Monari, Antonio; Rivail, Jean-Louis; Assfeld, Xavier

    2013-02-19

    Molecular mechanics methods can efficiently compute the macroscopic properties of a large molecular system but cannot represent the electronic changes that occur during a chemical reaction or an electronic transition. Quantum mechanical methods can accurately simulate these processes, but they require considerably greater computational resources. Because electronic changes typically occur in a limited part of the system, such as the solute in a molecular solution or the substrate within the active site of enzymatic reactions, researchers can limit the quantum computation to this part of the system. Researchers take into account the influence of the surroundings by embedding this quantum computation into a calculation of the whole system described at the molecular mechanical level, a strategy known as the mixed quantum mechanics/molecular mechanics (QM/MM) approach. The accuracy of this embedding varies according to the types of interactions included, whether they are purely mechanical or classically electrostatic. This embedding can also introduce the induced polarization of the surroundings. The difficulty in QM/MM calculations comes from the splitting of the system into two parts, which requires severing the chemical bonds that link the quantum mechanical subsystem to the classical subsystem. Typically, researchers replace the quantoclassical atoms, those at the boundary between the subsystems, with a monovalent link atom. For example, researchers might add a hydrogen atom when a C-C bond is cut. This Account describes another approach, the Local Self Consistent Field (LSCF), which was developed in our laboratory. LSCF links the quantum mechanical portion of the molecule to the classical portion using a strictly localized bond orbital extracted from a small model molecule for each bond. In this scenario, the quantoclassical atom has an apparent nuclear charge of +1. To achieve correct bond lengths and force constants, we must take into account the inner shell of

  12. Decoherence in quantum mechanics and quantum cosmology

    NASA Technical Reports Server (NTRS)

    Hartle, James B.

    1992-01-01

    A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.

  13. $\\cN$-FOLD SUPERSYMMETRY IN QUANTUM MECHANICAL MATRIX MODELS

    NASA Astrophysics Data System (ADS)

    Tanaka, Toshiaki

    2012-03-01

    We formulate Ņ-fold supersymmetry in quantum mechanical matrix models. As an example, we construct general two-by-two Hermitian matrix two-fold supersymmetric quantum mechanical systems. We find that there are two inequivalent such systems, both of which are characterized by two arbitrary scalar functions, and one of which does not reduce to the scalar system. The obtained systems are all weakly quasi-solvable.

  14. BOOK REVIEWS: Quantum Mechanics: Fundamentals

    NASA Astrophysics Data System (ADS)

    Whitaker, A.

    2004-02-01

    This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried’s well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Quantum mechanics was already solidly established by 1966, but this second edition gives an indication of progress made and changes in perspective over the last thirty-five years, and also recognises the very substantial increase in knowledge of quantum theory obtained at the undergraduate level. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Their practical importance has now been fully recognised, and a substantial account of them is provided in the new book. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. John Bell’s work of the mid-1960s has led to genuine theoretical and experimental achievement, which has facilitated the development of quantum optics and quantum information theory. Gottfried’s 1966 book played a modest part in this development. When Bell became increasingly irritated with the standard theoretical approach to quantum measurement, Viki Weisskopf repeatedly directed him to Gottfried’s book. Gottfried had devoted a

  15. BOOK REVIEWS: Quantum Mechanics: Fundamentals

    NASA Astrophysics Data System (ADS)

    Whitaker, A.

    2004-02-01

    This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried’s well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Quantum mechanics was already solidly established by 1966, but this second edition gives an indication of progress made and changes in perspective over the last thirty-five years, and also recognises the very substantial increase in knowledge of quantum theory obtained at the undergraduate level. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Their practical importance has now been fully recognised, and a substantial account of them is provided in the new book. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. John Bell’s work of the mid-1960s has led to genuine theoretical and experimental achievement, which has facilitated the development of quantum optics and quantum information theory. Gottfried’s 1966 book played a modest part in this development. When Bell became increasingly irritated with the standard theoretical approach to quantum measurement, Viki Weisskopf repeatedly directed him to Gottfried’s book. Gottfried had devoted a

  16. How quantum are non-negative wavefunctions?

    NASA Astrophysics Data System (ADS)

    Hastings, M. B.

    2016-01-01

    We consider wavefunctions which are non-negative in some tensor product basis. We study what possible teleportation can occur in such wavefunctions, giving a complete answer in some cases (when one system is a qubit) and partial answers elsewhere. We use this to show that a one-dimensional wavefunction which is non-negative and has zero correlation length can be written in a "coherent Gibbs state" form, as explained later. We conjecture that such holds in higher dimensions. Additionally, some results are provided on possible teleportation in general wavefunctions, explaining how Schmidt coefficients before measurement limit the possible Schmidt coefficients after measurement, and on the absence of a "generalized area law" [D. Aharonov et al., in Proceedings of Foundations of Computer Science (FOCS) (IEEE, 2014), p. 246; e-print arXiv.org:1410.0951] even for Hamiltonians with no sign problem. One of the motivations for this work is an attempt to prove a conjecture about ground state wavefunctions which have an "intrinsic" sign problem that cannot be removed by any quantum circuit. We show a weaker version of this, showing that the sign problem is intrinsic for commuting Hamiltonians in the same phase as the double semion model under the technical assumption that TQO-2 holds [S. Bravyi et al., J. Math. Phys. 51, 093512 (2010)].

  17. Quantum mechanics for applied physics and engineering

    NASA Astrophysics Data System (ADS)

    Fromhold, A. T., Jr.

    An introduction to quantum mechanics is provided, taking into account wave-particle duality, classical wave motion, the wave nature of particles the development of the time-dependent and time-independent Schroedinger wave equations, the wave-packet solutions and the uncertainty relation, and the expectation values for quantum-mechanical operators. Many-particle systems and quantum statistics are considered along with a free-electron model and the Boltzmann equation, the Wentzel-Kramers-Brillouin approximation and electron tunneling, perturbation theory, diffraction of valence electrons, and the nearly-free-electron model. The periodicity of crystalline solids is examined, and Bloch's theorem and energy bands for a periodic potential are discussed, giving attention to the periodic potential characteristic of the perfect monocrystal, the Hamiltonian for an electron in a periodic potential, and energy bands from the viewpoint of the one-electron atomic levels.

  18. Predicting crystal structure by merging data mining with quantum mechanics.

    PubMed

    Fischer, Christopher C; Tibbetts, Kevin J; Morgan, Dane; Ceder, Gerbrand

    2006-08-01

    Modern methods of quantum mechanics have proved to be effective tools to understand and even predict materials properties. An essential element of the materials design process, relevant to both new materials and the optimization of existing ones, is knowing which crystal structures will form in an alloy system. Crystal structure can only be predicted effectively with quantum mechanics if an algorithm to direct the search through the large space of possible structures is found. We present a new approach to the prediction of structure that rigorously mines correlations embodied within experimental data and uses them to direct quantum mechanical techniques efficiently towards the stable crystal structure of materials.

  19. A Local Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Lopez, Carlos

    2016-04-01

    A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the "virtual" paths in the path integral formalism, determining the output for measurement of position or momentum; second, a mathematical model for spin states, equivalent to the path integral formalism for point particles in space time, with the corresponding label. The mathematical machinery of orthodox quantum mechanics is maintained, in particular amplitudes of probability and Born's rule; therefore, Bell's type inequalities theorems do not apply. It is shown that statistical correlations for pairs of particles with entangled spins have a description completely equivalent to the two slit experiment, that is, interference (wave like behaviour) instead of non locality gives account of the process. The interpretation is grounded in the experimental evidence of a point like character of electrons, and in the hypothetical existence of a wave like, the de Broglie, companion system. A correspondence between the extended Hilbert spaces of hidden physical states and the orthodox quantum mechanical Hilbert space shows the mathematical equivalence of both theories. Paradoxical behaviour with respect to the action reaction principle is analysed, and an experimental set up, modified two slit experiment, proposed to look for the companion system.

  20. Hermeneutics, Underdetermination and Quantum Mechanics.

    ERIC Educational Resources Information Center

    Cushing, James T.

    1995-01-01

    States that the existence of an essential underdetermination in the interpretation of the formalism of quantum mechanics, in spite of the widespread belief that logic and empirical considerations alone demand an indeterministic world view in physics, legitimizes the analysis of hermeneutics in science education. (LZ)

  1. A Bit of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Oss, Stefano; Rosi, Tommaso

    2015-04-01

    We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many reasons why quantum mechanical systems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called "common sense" based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.

  2. The Use of Ab Initio Wavefunctions in Line-Shape Calculations for Water Vapor

    NASA Astrophysics Data System (ADS)

    Gamache, Robert R.; Lamouroux, Julien; Schwenke, David W.

    2014-06-01

    In semi-classical line-shape calculations, the internal motions of the colliding pair are treated via quantum mechanics and the collision trajectory is determined by classical dynamics. The quantum mechanical component, i.e. the determination of reduced matrix elements (RME) for the colliding pair, requires the wavefunctions of the radiating and the perturbing molecules be known. Here the reduced matrix elements for collisions in the ground vibrational state of water vapor are calculated by two methods and compared. First, wavefunctions determined by diagonalizing an effective (Watson) Hamiltonian are used to calculate the RMEs and, second, the ab initio wavefunctions of Partridge and Schwenke are used. While the ground vibrational state will yield the best approximation of the wavefunctions from the effective Hamiltonian approach, this study clearly identifies problems for states not included in the fit of the Hamiltonian and for extrapolated states. RMEs determined using ab initio wavefunctions use ˜100000 times more computational time; however, all ro-vibrational interactions are included. Hence, the ab initio approach will yield better RMEs as the number of vibrational quanta exchanged in the optical transition increases, resulting in improvements in calculated half-widths and line shifts. It is important to note that even for pure rotational transitions the use of ab initio wavefunctions will yield improved results.

  3. Quantum Mechanics and Narratability

    NASA Astrophysics Data System (ADS)

    Myrvold, Wayne C.

    2016-07-01

    As has been noted by several authors, in a relativistic context, there is an interesting difference between classical and quantum state evolution. For a classical system, a state history of a quantum system given along one foliation uniquely determines, without any consideration of the system's dynamics, a state history along any other foliation. This is not true for quantum state evolution; there are cases in which a state history along one foliation is compatible with multiple distinct state histories along some other, a phenomenon that David Albert has dubbed "non-narratability." In this article, we address the question of whether non-narratability is restricted to the sorts of special states that so far have been used to illustrate it. The results of the investigation suggest that there has been a misplaced emphasis on underdetermination of state histories; though this is generic for the special cases that have up until now been considered, involving bipartite systems in pure entangled states, it fails generically in cases in which more component systems are taken into account, and for bipartite systems that have some entanglement with their environment. For such cases, if we impose relativistic causality constraints on the evolution, then, except for very special states, a state history along one foliation uniquely determines a state history along any other. But this in itself is a marked difference between classical and quantum state evolution, because, in a classical setting, no considerations of dynamics at all are needed to go from a state history along one foliation to a state history along another.

  4. A new introductory quantum mechanics curriculum

    NASA Astrophysics Data System (ADS)

    Kohnle, Antje; Bozhinova, Inna; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth

    2014-01-01

    The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum-mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of the interpretive aspects of quantum mechanics and quantum information theory. This paper gives an overview of the resources available from the IOP website. The core text includes around 80 articles which are co-authored by leading experts, arranged in themes, and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is included in the resource. Solutions to activities are available to instructors. The resources can be used in a variety of ways, from being supplemental to existing courses to forming a complete programme.

  5. Treating time travel quantum mechanically

    NASA Astrophysics Data System (ADS)

    Allen, John-Mark A.

    2014-10-01

    The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilizing the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their nonlinearity and time-travel paradoxes. In particular, the "equivalent circuit model"—which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory—is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of alternate theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features—such as time-travel paradoxes, the ability to distinguish nonorthogonal states with certainty, and the ability to clone or delete arbitrary pure states—that are present with D-CTCs and P-CTCs. The problems with nonlinear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.

  6. Gravity and Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Blencowe, Miles

    The emergence of the macroscopic classical world from the microscopic quantum world is commonly understood to be a consequence of the fact that any given quantum system is open, unavoidably interacting with unobserved environmental degrees of freedom that will cause initial quantum superposition states of the system to decohere, resulting in classical mixtures of either-or alternatives. A fundamental question concerns how large a macroscopic object can be placed in a manifest quantum state, such as a center of mass quantum superposition state, under conditions where the effects of the interacting environmental degrees of freedom are reduced (i.e. in ultrahigh vacuum and at ultralow temperatures). Recent experiments have in fact demonstrated manifest quantum behavior in nano-to-micron-scale mechanical systems. Gravity has been invoked in various ways as playing a possible fundamental role in enforcing classicality of matter systems beyond a certain scale. Adopting the viewpoint that the standard perturbative quantization of general relativity provides an effective description of quantum gravity that is valid at ordinary energies, we show that it is possible to describe quantitatively how gravity as an environment can induce the decoherence of matter superposition states. The justification for such an approach follows from the fact that we are considering laboratory scale systems, where the matter is localized to regions of small curvature. As with other low energy effects, such as the quantum gravity correction to the Newtonian potential between two ordinary masses, it should be possible to quantitatively evaluate gravitationally induced decoherence rates by employing standard perturbative quantum gravity as an effective field theory; whatever the final form the eventual correct quantum theory of gravity takes, it must converge in its predictions with the effective field theory description at low energies. Research supported by the National Science Foundation (NSF

  7. Diagrammatic quantum mechanics

    NASA Astrophysics Data System (ADS)

    Kauffman, Louis H.; Lomonaco, Samuel J.

    2015-05-01

    This paper explores how diagrams of quantum processes can be used for modeling and for quantum epistemology. The paper is a continuation of the discussion where we began this formulation. Here we give examples of quantum networks that represent unitary transformations by dint of coherence conditions that constitute a new form of non-locality. Local quantum devices interconnected in space can form a global quantum system when appropriate coherence conditions are maintained.

  8. Engineering the quantum transport of atomic wavefunctions over macroscopic distances

    NASA Astrophysics Data System (ADS)

    Alberti, A.; Ivanov, V. V.; Tino, G. M.; Ferrari, G.

    2009-08-01

    The manipulation of matter waves had an important role in the history of quantum mechanics. The first experimental validation of matter-wave behaviour was the observation of diffraction of matter by crystals, followed by interference experiments with electrons, neutrons, atoms and molecules using gratings and Young's double slit. More recently, matter-wave manipulation has become a building block for quantum devices such as quantum sensors and it has an essential role in a number of proposals for implementing quantum computers. Here, we demonstrate the coherent control of the spatial extent of an atomic wavefunction by reversibly stretching and shrinking the wavefunction over a distance of more than one millimetre. The quantum-coherent process is fully deterministic, reversible and in quantitative agreement with an analytical model. The simplicity of its experimental implementation could ease applications in the field of quantum transport and quantum processing.

  9. PT quantum mechanics - Recent results

    NASA Astrophysics Data System (ADS)

    Bender, Carl M.

    2012-09-01

    Most quantum physicists believe that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under matrix transposition and complex conjugation) to be sure that the energy eigenvalues are real and that time evolution is unitary. However, the non-Dirac-hermitian Hamiltonian H = p2+ix3 has a real positive discrete spectrum and generates unitary time evolution and defines a fully consistent and physical quantum theory. Evidently, Dirac Hermiticity is too restrictive. While H = p2+ix3 is not Dirac Hermitian, it is PT symmetric (invariant under combined space reflection P and time reversal T). Another PT-symmetric Hamiltonian whose energy levels are real, positive and discrete is H = p2-x4, which contains an upside-down potential. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics and quantum field theory are extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past two years some of these properties have been verified in laboratory experiments. Here, we first discuss PT-symmetric Hamiltonians at a simple intuitive level and explain why the energy levels of such Hamiltonians may be real, positive, and discrete. Second, we describe a recent experiment in which the PT phase transition was observed. Third, we briefly mention that PT-symmetric theories can be useful at a fundamental level. While the double-scaling limit of an O(N)-symmetric gφ4 quantum field theory appears to be inconsistent because the critical value of g is negative, this limit is in fact not inconsistent because the critical theory is PT symmetric.

  10. Three-space from quantum mechanics

    SciTech Connect

    Chew, G.F.; Stapp, H.P.

    1988-08-01

    We formulate a discrete quantum-mechanical precursor to spacetime geometry. The objective is to provide the foundation for a quantum mechanics that is rooted exclusively in quantum-mechanical concepts, with all classical features, including the three-dimensional spatial continuum, emerging dynamically.

  11. Porphyrin Metalation at MgO Surfaces: A Spectroscopic and Quantum Mechanical Study on Complementary Model Systems.

    PubMed

    Schneider, Johannes; Franke, Matthias; Gurrath, Martin; Röckert, Michael; Berger, Thomas; Bernardi, Johannes; Meyer, Bernd; Steinrück, Hans-Peter; Lytken, Ole; Diwald, Oliver

    2016-01-26

    We show that both single-crystalline and nanostructured MgO surfaces convert free-base tetraphenyl porphyrin (2HTPP) into magnesium tetraphenyl porphyrin (MgTPP) at room temperature. The reaction can be viewed as an ion exchange between the two aminic protons of the 2HTPP molecule with a Mg(2+) ion from the surface. The driving force for the reaction is the strong stability of the formed hydroxyl groups along the steps and at defects on the MgO surface. We have used an integrated characterization approach that includes UV/Vis diffuse reflectance measurements on nanostructured powders, X-ray photoelectron spectroscopic investigation of atomically clean MgO(100) single-crystalline thin films, and density functional theory (DFT) calculations on model systems. The DFT calculations demonstrate that MgTPP formation is strongly exothermic at the corners, edges and steps, but slightly endothermic on terrace sites. This agrees well with the UV/Vis diffuse reflectance, which upon adsorption of 2HTPP shows a decrease in the absorption band associated with corner and edge sites on MgO nanocube powders. PMID:26682774

  12. Computations in quantum mechanics made easy

    NASA Astrophysics Data System (ADS)

    Korsch, H. J.; Rapedius, K.

    2016-09-01

    Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of spectral and dynamical properties for one-dimensional and two-dimensional single-particle systems as well as bosonic many-particle and open quantum systems. Due to their technical simplicity these methods are well suited as a tool for teaching quantum mechanics to undergraduates and graduates. Explicit implementations of the presented numerical methods in Matlab are given.

  13. Wave-function functionals

    SciTech Connect

    Pan Xiaoyin; Slamet, Marlina; Sahni, Viraht

    2010-04-15

    We extend our prior work on the construction of variational wave functions {psi} that are functionals of functions {chi}:{psi}={psi}[{chi}] rather than simply being functions. In this manner, the space of variations is expanded over those of traditional variational wave functions. In this article we perform the constrained search over the functions {chi} chosen such that the functional {psi}[{chi}] satisfies simultaneously the constraints of normalization and the exact expectation value of an arbitrary single- or two-particle Hermitian operator, while also leading to a rigorous upper bound to the energy. As such the wave function functional is accurate not only in the region of space in which the principal contributions to the energy arise but also in the other region of the space represented by the Hermitian operator. To demonstrate the efficacy of these ideas, we apply such a constrained search to the ground state of the negative ion of atomic hydrogen H{sup -}, the helium atom He, and its positive ions Li{sup +} and Be{sup 2+}. The operators W whose expectations are obtained exactly are the sum of the single-particle operators W={Sigma}{sub i}r{sub i}{sup n},n=-2,-1,1,2, W={Sigma}{sub i{delta}}(r{sub i}), W=-(1/2){Sigma}{sub i{nabla}i}{sup 2}, and the two-particle operators W={Sigma}{sub n}u{sup n},n=-2,-1,1,2, where u=|r{sub i}-r{sub j}|. Comparisons with the method of Lagrangian multipliers and of other constructions of wave-function functionals are made. Finally, we present further insights into the construction of wave-function functionals by studying a previously proposed construction of functionals {psi}[{chi}] that lead to the exact expectation of arbitrary Hermitian operators. We discover that analogous to the solutions of the Schroedinger equation, there exist {psi}[{chi}] that are unphysical in that they lead to singular values for the expectations. We also explain the origin of the singularity.

  14. Deformed Conformal and Supersymmetric Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Spiridonov, Vyacheslav

    Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e., the spectrum of one can be obtained from another (with possible exception of the lowest level) by the q2-factor scaling. A special class of the self-similar potentials is shown to obey the dynamical conformal symmetry algebra suq(1,1). These potentials exhibit exponential spectra and corresponding raising and lowering operators satisfy the q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane.

  15. A Primer on Resonances in Quantum Mechanics

    SciTech Connect

    Rosas-Ortiz, Oscar; Fernandez-Garcia, Nicolas; Cruz y Cruz, Sara

    2008-11-13

    After a pedagogical introduction to the concept of resonance in classical and quantum mechanics, some interesting applications are discussed. The subject includes resonances occurring as one of the effects of radiative reaction, the resonances involved in the refraction of electromagnetic waves by a medium with a complex refractive index, and quantum decaying systems described in terms of resonant states of the energy (Gamow-Siegert functions). Some useful mathematical approaches like the Fourier transform, the complex scaling method and the Darboux transformation are also reviewed.

  16. Quantum mechanics of two relativistic bound fermions

    SciTech Connect

    Giachetti, R.; Sorace, E.

    2006-11-15

    This presentation shows how a joint use of symbolic and numerical programming makes it possible the construction of new quantum mechanical models and the explicit solution for their spectra. Similar methods can be used for investigating quantum systems of different nature with the highest accuracy, as it can be required by the development of new technologies. In particular we deal with the quantization of two relativistic fermions of arbitrary masses interacting by means of a radial potential. The numerical results are given for the Coulomb interaction.

  17. Supersymmetric quantum mechanics and its applications

    SciTech Connect

    Sukumar, C.V.

    2004-12-23

    The Hamiltonian in Supersymmetric Quantum Mechanics is defined in terms of charges that obey the same algebra as that of the generators of supersymmetry in field theory. The consequences of this symmetry for the spectra of the component parts that constitute the supersymmetric system are explored. The implications of supersymmetry for the solutions of the Schroedinger equation, the Dirac equation, the inverse scattering theory and the multi-soliton solutions of the KdV equation are examined. Applications to scattering problems in Nuclear Physics with specific reference to singular potentials which arise from considerations of supersymmetry will be discussed.

  18. Ultrafast dynamics of many-body processes and fundamental quantum mechanical phenomena in semiconductors

    PubMed Central

    Chemla, Daniel S.; Shah, Jagdeep

    2000-01-01

    The large dielectric constant and small effective mass in a semiconductor allows a description of its electronic states in terms of envelope wavefunctions whose energy, time, and length scales are mesoscopic, i.e., halfway between those of atomic and those of condensed matter systems. This property makes it possible to demonstrate and investigate many quantum mechanical, many-body, and quantum kinetic phenomena with tabletop experiments that would be nearly impossible in other systems. This, along with the ability to custom-design semiconductor nanostructures, makes semiconductors an ideal laboratory for experimental investigations. We present an overview of some of the most exciting results obtained in semiconductors in recent years using the technique of ultrafast nonlinear optical spectrocopy. These results show that Coulomb correlation plays a major role in semiconductors and makes them behave more like a strongly interacting system than like an atomic system. The results provide insights into the physics of strongly interacting systems that are relevant to other condensed matter systems, but not easily accessible in other materials. PMID:10716981

  19. An improved fragment-based quantum mechanical method for calculation of electrostatic solvation energy of proteins.

    PubMed

    Jia, Xiangyu; Wang, Xianwei; Liu, Jinfeng; Zhang, John Z H; Mei, Ye; He, Xiao

    2013-12-01

    An efficient approach that combines the electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method with conductor-like polarizable continuum model (CPCM), termed EE-GMFCC-CPCM, is developed for ab initio calculation of the electrostatic solvation energy of proteins. Compared with the previous MFCC-CPCM study [Y. Mei, C. G. Ji, and J. Z. H. Zhang, J. Chem. Phys. 125, 094906 (2006)], quantum mechanical (QM) calculation is applied to deal with short-range non-neighboring interactions replacing the classical treatment. Numerical studies are carried out for proteins up to 3837 atoms at the HF/6-31G* level. As compared to standard full system CPCM calculations, EE-GMFCC-CPCM shows clear improvement over the MFCC-CPCM method for both the total electrostatic solvation energy and its components (the polarized solute-solvent reaction field energy and wavefunction distortion energy of the solute). For large proteins with 1000-4000 atoms, where the standard full system ab initio CPCM calculations are not affordable, the EE-GMFCC-CPCM gives larger relative wavefunction distortion energies and weaker relative electrostatic solvation energies for proteins, as compared to the corresponding energies calculated by the Divide-and-Conquer Poisson-Boltzmann (D&C-PB) method. Notwithstanding, a high correlation between EE-GMFCC-CPCM and D&C-PB is observed. This study demonstrates that the linear-scaling EE-GMFCC-CPCM approach is an accurate and also efficient method for the calculation of electrostatic solvation energy of proteins.

  20. Minkowski Space and Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    O'Hara, Paul

    A paradigm shift distinguishes general relativity from classical mechanics. In general relativity the energy-momentum tensor is the effective cause of the ontological space-time curvature and vice-versa, while in classical physics, the structure of space-time is treated as an accidental cause, serving only as a backdrop against which the laws of physics unfold. This split in turn is inherited by quantum mechanics, which is usually developed by changing classical (including special relativity) Hamiltonians into quantum wave equations.

  1. Quantum mechanics and reality: An interpretation of Everett's theory

    NASA Astrophysics Data System (ADS)

    Lehner, Christoph Albert

    The central part of Everett's formulation of quantum mechanics is a quantum mechanical model of memory and of observation as the recording of information in a memory. To use this model as an answer to the measurement problem, Everett has to assume that a conscious observer can be in a superposition of such memory states and be unaware of it. This assumption has puzzled generations of readers. The fundamental aim of this dissertation is to find a set of simpler assumptions which are sufficient to show that Everett's model is empirically adequate. I argue that Everett's model needs three assumptions to account for the process of observation: an assumption of decoherence of observers as quantum mechanical systems; an assumption of supervenience of mental states (qualities) over quantum mechanical properties; and an assumption about the interpretation of quantum mechanical states in general: quantum mechanical states describe ensembles of states of affairs coexisting in the same system. I argue that the only plausible understanding of such ensembles is as ensembles of possibilities, and that all standard no-collapse interpretations agree in this reading of quantum mechanical states. Their differences can be understood as different theories about what marks the real state within this ensemble, and Everett's theory as the claim that no additional 'mark of reality' is necessary. Using the three assumptions, I argue that introspection cannot determine the objective quantum mechanical state of an observer. Rather, the introspective qualities of a quantum mechanical state can be represented by a (classical) statistical ensemble of subjective states. An analysis of these subjective states and their dynamics leads to the conclusion that they suffice to give empirically correct predictions. The argument for the empirical adequacy of the subjective state entails that knowledge of the objective quantum mechanical state is impossible in principle. Empirical reality for a conscious

  2. Hadronic wavefunctions in light-cone quantization

    SciTech Connect

    Hyer, T.

    1994-05-01

    The analysis of light-cone wavefunctions seems the most promising theoretical approach to a detailed understanding of the structure of relativistic bound states, particularly hadrons. However, there are numerous complications in this approach. Most importantly, the light-cone approach sacrifices manifest rotational invariance in exchange for the elimination of negative-energy states. The requirement of rotational invariance of the full theory places important constraints on proposed light-cone wavefunctions, whether they are modelled or extracted from some numerical procedure. A formulation of the consequences of the hidden rotational symmetry has been sought for some time; it is presented in Chapter 2. In lattice gauge theory or heavy-quark effective theory, much of the focus is on the extraction of numerical values of operators which are related to the hadronic wavefunction. These operators are to some extent interdependent, with relations induced by fundamental constraints on the underlying wavefunction. The consequences of the requirement of unitarity are explored in Chapter 3, and are found to have startling phenomenological relevance. To test model light-cone wavefunctions, experimental predictions must be made. The reliability of perturbative QCD as a tool for making such predictions has been questioned. In Chapter 4, the author presents a computation of the rates for nucleon-antinucleon annihilation, improving the reliability of the perturbative computation by taking into account the Sudakov suppression of exclusive processes at large transverse impact parameter. In Chapter 5, he develops the analysis of semiexclusive production. This work focuses on processes in which a single isolated meson is produced perturbatively and recoils against a wide hadronizing system. At energies above about 10 GeV, semiexclusive processes are shown to be the most sensitive experimental probes of hadronic structure.

  3. Space and time from quantum mechanics

    NASA Astrophysics Data System (ADS)

    Chew, G. F.

    1992-09-01

    Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over the collapse of the quantum-mechanical state vector when measurement is performed. Additionally, the pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as a coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.

  4. Space and time from quantum mechanics

    SciTech Connect

    Chew, G.F.

    1992-09-16

    Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over collapse of the quantum-mechanical state vector when measurement is performed. Additionally, pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.

  5. N=4 supersymmetric multidimensional quantum mechanics, partial SUSY breaking, and superconformal quantum mechanics

    NASA Astrophysics Data System (ADS)

    Donets, E. E.; Pashnev, A.; Juan Rosales, J.; Tsulaia, M. M.

    2000-02-01

    The multidimensional N=4 supersymmetric (SUSY) quantum mechanics (QM) is constructed using the superfield approach. As a result, the component form of the classical and quantum Lagrangian and Hamiltonian is obtained. In the SUSY QM considered, both classical and quantum N=4 algebras include central charges, and this opens various possibilities for partial supersymmetry breaking. It is shown that quantum-mechanical models with one-quarter, one-half, and three-quarters of unbroken (broken) supersymmetries can exist in the framework of the multidimensional N=4 SUSY QM, while the one-dimensional N=4 SUSY QM, constructed earlier, admits only one half or total supersymmetry breakdown. We illustrate the constructed general formalism, as well as all possible cases of partial SUSY breaking taking as an example a direct multidimensional generalization of the one-dimensional N=4 superconformal quantum-mechanical model. Some open questions and possible applications of the constructed multidimensional N=4 SUSY QM to the known exactly integrable systems and problems of quantum cosmology are briefly discussed.

  6. Hidden variables and nonlocality in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Hemmick, Douglas Lloyd

    1997-05-01

    Most physicists hold a skeptical attitude toward a 'hidden variables' interpretation of quantum theory, despite David Bohm's successful construction of such a theory and John S. Bell's strong arguments in favor of the idea. The first reason for doubt concerns certain mathematical theorems (von Neumann's, Gleason's, Kochen and Specker's, and Bell's) which can be applied to the hidden variables issue. These theorems are often credited with proving that hidden variables are indeed 'impossible', in the sense that they cannot replicate the predictions of quantum mechanics. Many who do not draw such a strong conclusion nevertheless accept that hidden variables have been shown to exhibit prohibitively complicated features. The second concern is that the most sophisticated example of a hidden variables theory-that of David Bohm-exhibits non-locality, i.e., consequences of events at one place can propagate to other places instantaneously. However, neither the mathematical theorems in question nor the attribute of nonlocality detract from the importance of a hidden variables interpretation of quantum theory. Nonlocality is present in quantum mechanics itself, and is a required characteristic of any theory that agrees with the quantum mechanical predictions. We first discuss the earliest analysis of hidden variables-that of von Neumann's theorem-and review John S. Bell's refutation of von Neumann's 'impossibility proof'. We recall and elaborate on Bell's arguments regarding the theorems of Gleason, and Kochen and Specker. According to Bell, these latter theorems do not imply that hidden variables interpretations are untenable, but instead that such theories must exhibit contextuality, i.e., they must allow for the dependence of measurement results on the characteristics of both measured system and measuring apparatus. We demonstrate a new way to understand the implications of both Gleason's theorem and Kochen and Specker's theorem by noting that they prove a result we call

  7. Heisenberg and the Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Camilleri, Kristian

    2009-02-01

    Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.

  8. Heisenberg and the Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Camilleri, Kristian

    2011-09-01

    Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.

  9. Facets of contextual realism in quantum mechanics

    SciTech Connect

    Pan, Alok Kumar; Home, Dipankar

    2011-09-23

    In recent times, there is an upsurge of interest in demonstrating the quantum contextuality. In this proceedings, we explore the two different forms of arguments that have been used for showing the contextual character of quantum mechanics. First line of study concerns the violations of the noncontextual realist models by quantum mechanics, where second line of study that is qualitatively distinct from the earlier one, demonstrates the contextuality within the formalism of quantum mechanics.

  10. Measurement and Fundamental Processes in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Jaeger, Gregg

    2015-07-01

    In the standard mathematical formulation of quantum mechanics, measurement is an additional, exceptional fundamental process rather than an often complex, but ordinary process which happens also to serve a particular epistemic function: during a measurement of one of its properties which is not already determined by a preceding measurement, a measured system, even if closed, is taken to change its state discontinuously rather than continuously as is usual. Many, including Bell, have been concerned about the fundamental role thus given to measurement in the foundation of the theory. Others, including the early Bohr and Schwinger, have suggested that quantum mechanics naturally incorporates the unavoidable uncontrollable disturbance of physical state that accompanies any local measurement without the need for an exceptional fundamental process or a special measurement theory. Disturbance is unanalyzable for Bohr, but for Schwinger it is due to physical interactions' being borne by fundamental particles having discrete properties and behavior which is beyond physical control. Here, Schwinger's approach is distinguished from more well known treatments of measurement, with the conclusion that, unlike most, it does not suffer under Bell's critique of quantum measurement. Finally, Schwinger's critique of measurement theory is explicated as a call for a deeper investigation of measurement processes that requires the use of a theory of quantum fields.

  11. Symmetry as a foundational concept in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Ziaeepour, Houri

    2015-07-01

    Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a fundamental concept in the construction of physical systems. Based on this idea, we propose a series of postulates for describing quantum systems, and establish their relation and correspondence with axioms of standard quantum mechanics. Through some examples we show that this reformulation helps better understand some of ambiguities of standard description. Nonetheless its application is not limited to explaining confusing concept and it may be a necessary step toward a consistent model of quantum cosmology and gravity.

  12. Study on a Possible Darwinian Origin of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Baladrón, C.

    2011-03-01

    A sketchy subquantum theory deeply influenced by Wheeler's ideas (Am. J. Phys. 51:398-404, 1983) and by the de Broglie-Bohm interpretation (Goldstein in Stanford Encyclopedia of Philosophy, 2006) of quantum mechanics is further analyzed. In this theory a fundamental system is defined as a dual entity formed by bare matter and a methodological probabilistic classical Turing machine. The evolution of the system would be determined by three Darwinian informational regulating principles. Some progress in the derivation of the postulates of quantum mechanics from these regulating principles is reported. The entanglement in a bipartite system is preliminarily considered.

  13. Deformation of noncommutative quantum mechanics

    NASA Astrophysics Data System (ADS)

    Jiang, Jian-Jian; Chowdhury, S. Hasibul Hassan

    2016-09-01

    In this paper, the Lie group GNC α , β , γ , of which the kinematical symmetry group GNC of noncommutative quantum mechanics (NCQM) is a special case due to fixed nonzero α, β, and γ, is three-parameter deformation quantized using the method suggested by Ballesteros and Musso [J. Phys. A: Math. Theor. 46, 195203 (2013)]. A certain family of QUE algebras, corresponding to GNC α , β , γ with two of the deformation parameters approaching zero, is found to be in agreement with the existing results of the literature on quantum Heisenberg group. Finally, we dualize the underlying QUE algebra to obtain an expression for the underlying star-product between smooth functions on GNC α , β , γ .

  14. Kindergarten Quantum Mechanics: Lecture Notes

    SciTech Connect

    Coecke, Bob

    2006-01-04

    These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns 'doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I which subsumes my Logic of Entanglement. For a survey on the 'what', the 'why' and the 'hows' I refer to a previous set of lecture notes. In a last section we provide some pointers to the body of technical literature on the subject.

  15. Communication: Unambiguous comparison of many-electron wavefunctions through their overlaps

    NASA Astrophysics Data System (ADS)

    Plasser, Felix; González, Leticia

    2016-07-01

    A simple and powerful method for comparing many-electron wavefunctions constructed at different levels of theory is presented. By using wavefunction overlaps, it is possible to analyze the effects of varying wavefunction models, molecular orbitals, and one-electron basis sets. The computation of wavefunction overlaps eliminates the inherent ambiguity connected to more rudimentary wavefunction analysis protocols, such as visualization of orbitals or comparing selected physical observables. Instead, wavefunction overlaps allow processing the many-electron wavefunctions in their full inherent complexity. The presented method is particularly effective for excited state calculations as it allows for automatic monitoring of changes in the ordering of the excited states. A numerical demonstration based on multireference computations of two test systems, the selenoacrolein molecule and an iridium complex, is presented.

  16. proper versus improper mixtures: Toward a quaternionic quantum mechanics

    NASA Astrophysics Data System (ADS)

    Masillo, F.; Scolarici, G.; Sozzo, S.

    2009-07-01

    The density operators obtained by taking partial traces represent improper mixtures of subsystems of a compound physical system because the coefficients in the convex sums expressing them never bear the ignorance interpretation. Assigning states to these subsystems is consequently problematic in standard quantum mechanics (subentity problem). In the semantic realism interpretation of quantum mechanics, it is instead proposed to consider improper mixtures true nonpure states conceptually distinct from proper mixtures. Based on this proposal, we show that proper and improper mixtures can be represented by different density operators in the quaternionic formulation of quantum mechanics and can hence be distinguished even from a mathematical standpoint. We provide a simple example related to the quantum theory of measurement.

  17. Quantum Mechanics with a Little Less Mystery

    ERIC Educational Resources Information Center

    Cropper, William H.

    1969-01-01

    Suggests the "route of the inquiring mind in presenting the esoteric quantum mechanical postulates and concepts in an understandable form. Explains that the quantum mechanical postulates are but useful mathematical forms to express thebroader principles of superposition and correspondence. Briefly describes some of the features which makes the…

  18. Teaching Quantum Mechanics on an Introductory Level.

    ERIC Educational Resources Information Center

    Muller, Rainer; Wiesner, Hartmut

    2002-01-01

    Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)

  19. Quantum Mechanical Earth: Where Orbitals Become Orbits

    ERIC Educational Resources Information Center

    Keeports, David

    2012-01-01

    Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…

  20. Statistical mechanics based on fractional classical and quantum mechanics

    SciTech Connect

    Korichi, Z.; Meftah, M. T.

    2014-03-15

    The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantum mechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantum mechanics, we have calculated the thermodynamical properties for the black body radiation, studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac statistics.

  1. An axiomatic formulation of the Montevideo interpretation of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Gambini, Rodolfo; García-Pintos, Luis Pedro; Pullin, Jorge

    We make a first attempt to axiomatically formulate the Montevideo interpretation of quantum mechanics. In this interpretation environmental decoherence is supplemented with loss of coherence due to the use of realistic clocks to measure time to solve the measurement problem. The resulting formulation is framed entirely in terms of quantum objects. Unlike in ordinary quantum mechanics, classical time only plays the role of an unobservable parameter. The formulation eliminates any privileged role of the measurement process giving an objective definition of when an event occurs in a system.

  2. Quantum mechanical effects in plasmonic structures with subnanometre gaps

    NASA Astrophysics Data System (ADS)

    Zhu, Wenqi; Esteban, Ruben; Borisov, Andrei G.; Baumberg, Jeremy J.; Nordlander, Peter; Lezec, Henri J.; Aizpurua, Javier; Crozier, Kenneth B.

    2016-06-01

    Metallic structures with nanogap features have proven highly effective as building blocks for plasmonic systems, as they can provide a wide tuning range of operating frequencies and large near-field enhancements. Recent work has shown that quantum mechanical effects such as electron tunnelling and nonlocal screening become important as the gap distances approach the subnanometre length-scale. Such quantum effects challenge the classical picture of nanogap plasmons and have stimulated a number of theoretical and experimental studies. This review outlines the findings of many groups into quantum mechanical effects in nanogap plasmons, and discusses outstanding challenges and future directions.

  3. Quantum mechanical effects in plasmonic structures with subnanometre gaps

    PubMed Central

    Zhu, Wenqi; Esteban, Ruben; Borisov, Andrei G.; Baumberg, Jeremy J.; Nordlander, Peter; Lezec, Henri J.; Aizpurua, Javier; Crozier, Kenneth B.

    2016-01-01

    Metallic structures with nanogap features have proven highly effective as building blocks for plasmonic systems, as they can provide a wide tuning range of operating frequencies and large near-field enhancements. Recent work has shown that quantum mechanical effects such as electron tunnelling and nonlocal screening become important as the gap distances approach the subnanometre length-scale. Such quantum effects challenge the classical picture of nanogap plasmons and have stimulated a number of theoretical and experimental studies. This review outlines the findings of many groups into quantum mechanical effects in nanogap plasmons, and discusses outstanding challenges and future directions. PMID:27255556

  4. Quantum mechanical Hamiltonian models of discrete processes

    SciTech Connect

    Benioff, P.

    1981-03-01

    Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement.

  5. Quantum mechanical calculations to chemical accuracy

    NASA Technical Reports Server (NTRS)

    Bauschlicher, Charles W., Jr.; Langhoff, Stephen R.

    1991-01-01

    The accuracy of current molecular-structure calculations is illustrated with examples of quantum mechanical solutions for chemical problems. Two approaches are considered: (1) the coupled-cluster singles and doubles (CCSD) with a perturbational estimate of the contribution of connected triple excitations, or CCDS(T); and (2) the multireference configuration-interaction (MRCI) approach to the correlation problem. The MRCI approach gains greater applicability by means of size-extensive modifications such as the averaged-coupled pair functional approach. The examples of solutions to chemical problems include those for C-H bond energies, the vibrational frequencies of O3, identifying the ground state of Al2 and Si2, and the Lewis-Rayleigh afterglow and the Hermann IR system of N2. Accurate molecular-wave functions can be derived from a combination of basis-set saturation studies and full configuration-interaction calculations.

  6. ``the Human BRAIN & Fractal quantum mechanics''

    NASA Astrophysics Data System (ADS)

    Rosary-Oyong, Se, Glory

    In mtDNA ever retrieved from Iman Tuassoly, et.al:Multifractal analysis of chaos game representation images of mtDNA''.Enhances the price & valuetales of HE. Prof. Dr-Ing. B.J. HABIBIE's N-219, in J. Bacteriology, Nov 1973 sought:'' 219 exist as separate plasmidDNA species in E.coli & Salmonella panama'' related to ``the brain 2 distinct molecular forms of the (Na,K)-ATPase..'' & ``neuron maintains different concentration of ions(charged atoms'' thorough Rabi & Heisenber Hamiltonian. Further, after ``fractal space time are geometric analogue of relativistic quantum mechanics''[Ord], sought L.Marek Crnjac: ``Chaotic fractals at the root of relativistic quantum physics''& from famous Nottale: ``Scale relativity & fractal space-time:''Application to Quantum Physics , Cosmology & Chaotic systems'',1995. Acknowledgements to HE. Mr. H. TUK SETYOHADI, Jl. Sriwijaya Raya 3, South-Jakarta, INDONESIA.

  7. Effective equations for the quantum pendulum from momentous quantum mechanics

    SciTech Connect

    Hernandez, Hector H.; Chacon-Acosta, Guillermo

    2012-08-24

    In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.

  8. Student Understanding of Time Dependence in Quantum Mechanics

    ERIC Educational Resources Information Center

    Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.

    2015-01-01

    The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…

  9. Speakable and Unspeakable in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Bell, J. S.; Aspect, Introduction by Alain

    2004-06-01

    List of papers on quantum philosophy by J. S. Bell; Preface; Acknowledgements; Introduction by Alain Aspect; 1. On the problem of hidden variables in quantum mechanics; 2. On the Einstein-Rosen-Podolsky paradox; 3. The moral aspects of quantum mechanics; 4. Introduction to the hidden-variable question; 5. Subject and object; 6. On wave packet reduction in the Coleman-Hepp model; 7. The theory of local beables; 8. Locality in quantum mechanics: reply to critics; 9. How to teach special relativity; 10. Einstein-Podolsky-Rosen experiments; 11. The measurement theory of Everett and de Broglie's pilot wave; 12. Free variables and local causality; 13. Atomic-cascade photons and quantum-mechanical nonlocality; 14. de Broglie-Bohm delayed choice double-slit experiments and density matrix; 15. Quantum mechanics for cosmologists; 16. Bertlmann's socks and the nature of reality; 17. On the impossible pilot wave; 18. Speakable and unspeakable in quantum mechanics; 19. Beables for quantum field theory; 20. Six possible worlds of quantum mechanics; 21. EPR correlations and EPR distributions; 22. Are there quantum jumps?; 23. Against 'measurement'; 24. La Nouvelle cuisine.

  10. A multiscale quantum mechanics/electromagnetics method for device simulations.

    PubMed

    Yam, ChiYung; Meng, Lingyi; Zhang, Yu; Chen, GuanHua

    2015-04-01

    Multiscale modeling has become a popular tool for research applying to different areas including materials science, microelectronics, biology, chemistry, etc. In this tutorial review, we describe a newly developed multiscale computational method, incorporating quantum mechanics into electronic device modeling with the electromagnetic environment included through classical electrodynamics. In the quantum mechanics/electromagnetics (QM/EM) method, the regions of the system where active electron scattering processes take place are treated quantum mechanically, while the surroundings are described by Maxwell's equations and a semiclassical drift-diffusion model. The QM model and the EM model are solved, respectively, in different regions of the system in a self-consistent manner. Potential distributions and current densities at the interface between QM and EM regions are employed as the boundary conditions for the quantum mechanical and electromagnetic simulations, respectively. The method is illustrated in the simulation of several realistic systems. In the case of junctionless field-effect transistors, transfer characteristics are obtained and a good agreement between experiments and simulations is achieved. Optical properties of a tandem photovoltaic cell are studied and the simulations demonstrate that multiple QM regions are coupled through the classical EM model. Finally, the study of a carbon nanotube-based molecular device shows the accuracy and efficiency of the QM/EM method.

  11. Thermodynamic integration from classical to quantum mechanics

    SciTech Connect

    Habershon, Scott; Manolopoulos, David E.

    2011-12-14

    We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.

  12. Quantum Mechanical Methods for Enzyme Kinetics

    NASA Astrophysics Data System (ADS)

    Gao, Jiali; Truhlar, Donald G.

    2002-10-01

    This review discusses methods for the incorporation of quantum mechanical effects into enzyme kinetics simulations in which the enzyme is an explicit part of the model. We emphasize three aspects: (a) use of quantum mechanical electronic structure methods such as molecular orbital theory and density functional theory, usually in conjunction with molecular mechanics; (b) treating vibrational motions quantum mechanically, either in an instantaneous harmonic approximation, or by path integrals, or by a three-dimensional wave function coupled to classical nuclear motion; (c) incorporation of multidimensional tunneling approximations into reaction rate calculations.

  13. Improving student understanding of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Singh, Chandralekha

    2015-04-01

    Learning quantum mechanics is challenging for many students. We are investigating the difficulties that upper-level students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) and tools for peer-instruction. Many of the QuILTs employ computer simulations to help students visualize and develop better intuition about quantum phenomena. We will discuss the common students' difficulties and research-based tools we are developing to bridge the gap between quantitative and conceptual aspects of quantum mechanics and help students develop a solid grasp of quantum concepts. Support from the National Science Foundation is gratefully acknowledged.

  14. Improving students' understanding of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Singh, Chandralekha; Zhu, Guangtian

    2010-02-01

    Learning quantum mechanics is challenging. We are investigating the difficulties that upper-level students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) and tools for peer-instruction. Many of the QuILTs employ computer simulations to help students visualize and develop better intuition about quantum phenomena. We will discuss the common students' difficulties and research-based tools we are developing to bridge the gap between quantitative and conceptual aspects of quantum mechanics and help students develop a solid grasp of quantum concepts. Supported by the National Science Foundation. )

  15. Time as an Observable in Nonrelativistic Quantum Mechanics

    NASA Technical Reports Server (NTRS)

    Hahne, G. E.

    2003-01-01

    The argument follows from the viewpoint that quantum mechanics is taken not in the usual form involving vectors and linear operators in Hilbert spaces, but as a boundary value problem for a special class of partial differential equations-in the present work, the nonrelativistic Schrodinger equation for motion of a structureless particle in four- dimensional space-time in the presence of a potential energy distribution that can be time-as well as space-dependent. The domain of interest is taken to be one of two semi-infinite boxes, one bounded by two t=constant planes and the other by two t=constant planes. Each gives rise to a characteristic boundary value problem: one in which the initial, input values on one t=constant wall are given, with zero asymptotic wavefunction values in all spatial directions, the output being the values on the second t=constant wall; the second with certain input values given on both z=constant walls, with zero asymptotic values in all directions involving time and the other spatial coordinates, the output being the complementary values on the z=constant walls. The first problem corresponds to ordinary quantum mechanics; the second, to a fully time-dependent version of a problem normally considered only for the steady state (time-independent Schrodinger equation). The second problem is formulated in detail. A conserved indefinite metric is associated with space-like propagation, where the sign of the norm of a unidirectional state corresponds to its spatial direction of travel.

  16. Tips and Tools for Teaching Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Zhu, Guangtian; Singh, Chandralekha

    2009-03-01

    Learning quantum mechanics is challenging -- students usually struggle to master the basic concepts, even though they may perform well on solving quantitative problems. Our group is investigating the difficulties that upper-level students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are designing quantum interactive learning tutorials (QuILTs) and tools for peer-instruction. Many of the tutorials employ computer simulations to help students visualize and develop better intuition about quantum phenomena. We will discuss the common students' difficulties, share the material we have developed and evaluated to make the quantum mechanics class engaging and useful, and show ways to bridge the gap between quantitative and conceptual aspects of quantum mechanics.

  17. Supersymmetric q-deformed quantum mechanics

    SciTech Connect

    Traikia, M. H.; Mebarki, N.

    2012-06-27

    A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.

  18. Quantum mechanical stabilization of Minkowski signature wormholes

    SciTech Connect

    Visser, M.

    1989-05-19

    When one attempts to construct classical wormholes in Minkowski signature Lorentzian spacetimes violations of both the weak energy hypothesis and averaged weak energy hypothesis are encountered. Since the weak energy hypothesis is experimentally known to be violated quantum mechanically, this suggests that a quantum mechanical analysis of Minkowski signature wormholes is in order. In this note I perform a minisuperspace analysis of a simple class of Minkowski signature wormholes. By solving the Wheeler-de Witt equation for pure Einstein gravity on this minisuperspace the quantum mechanical wave function of the wormhole is obtained in closed form. The wormhole is shown to be quantum mechanically stabilized with an average radius of order the Planck length. 8 refs.

  19. Fundamental Quantum Mechanics--A Graphic Presentation

    ERIC Educational Resources Information Center

    Wise, M. N.; Kelley, T. G.

    1977-01-01

    Describes a presentation of basic quantum mechanics for nonscience majors that relies on a computer-generated graphic display to circumvent the usual mathematical difficulties. It allows a detailed treatment of free-particle motion in a wave picture. (MLH)

  20. Quantum mechanics: Thought experiments made real

    NASA Astrophysics Data System (ADS)

    Martín, Fernando

    2015-02-01

    Elegant experiments performed with X-rays and a double slit formed from molecular oxygen have finally made it possible to realize and test a long-standing and famous gedanken experiment in quantum mechanics.

  1. Classical Mechanics as Nonlinear Quantum Mechanics

    SciTech Connect

    Nikolic, Hrvoje

    2007-12-03

    All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schroedinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics.

  2. Adiabatic continuity, wave-function overlap, and topological phase transitions

    NASA Astrophysics Data System (ADS)

    Gu, Jiahua; Sun, Kai

    2016-09-01

    In this paper, we study the relation between wave-function overlap and adiabatic continuity in gapped quantum systems. We show that for two band insulators, a scalar function can be defined in the momentum space, which characterizes the wave-function overlap between Bloch states in the two insulators. If this overlap is nonzero for all momentum points in the Brillouin zone, these two insulators are adiabatically connected, i.e., we can deform one insulator into the other smoothly without closing the band gap. In addition, we further prove that this adiabatic path preserves all the symmetries of the insulators. The existence of such an adiabatic path implies that two insulators with nonzero wave-function overlap belong to the same topological phase. This relation, between adiabatic continuity and wave-function overlap, can be further generalized to correlated systems. The generalized relation cannot be applied to study generic many-body systems in the thermodynamic limit, because of the orthogonality catastrophe. However, for certain interacting systems (e.g., quantum Hall systems), the quantum wave-function overlap can be utilized to distinguish different quantum states. Experimental implications are also discussed.

  3. Causal localizations in relativistic quantum mechanics

    SciTech Connect

    Castrigiano, Domenico P. L. Leiseifer, Andreas D.

    2015-07-15

    Causal localizations describe the position of quantum systems moving not faster than light. They are constructed for the systems with finite spinor dimension. At the center of interest are the massive relativistic systems. For every positive mass, there is the sequence of Dirac tensor-localizations, which provides a complete set of inequivalent irreducible causal localizations. They obey the principle of special relativity and are fully Poincaré covariant. The boosters are determined by the causal position operator and the other Poincaré generators. The localization with minimal spinor dimension is the Dirac localization. Thus, the Dirac equation is derived here as a mere consequence of the principle of causality. Moreover, the higher tensor-localizations, not known so far, follow from Dirac’s localization by a simple construction. The probability of localization for positive energy states results to be described by causal positive operator valued (PO-) localizations, which are the traces of the causal localizations on the subspaces of positive energy. These causal Poincaré covariant PO-localizations for every irreducible massive relativistic system were, all the more, not known before. They are shown to be separated. Hence, the positive energy systems can be localized within every open region by a suitable preparation as accurately as desired. Finally, the attempt is made to provide an interpretation of the PO-localization operators within the frame of conventional quantum mechanics attributing an important role to the negative energy states.

  4. Quantum mechanical force field for water with explicit electronic polarization

    PubMed Central

    Han, Jaebeom; Mazack, Michael J. M.; Zhang, Peng; Truhlar, Donald G.; Gao, Jiali

    2013-01-01

    A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 106 self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across

  5. Quantum mechanical force field for water with explicit electronic polarization.

    PubMed

    Han, Jaebeom; Mazack, Michael J M; Zhang, Peng; Truhlar, Donald G; Gao, Jiali

    2013-08-01

    A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 10(6) self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across

  6. Selection of active spaces for multiconfigurational wavefunctions

    SciTech Connect

    Keller, Sebastian; Boguslawski, Katharina; Reiher, Markus; Janowski, Tomasz; Pulay, Peter

    2015-06-28

    The efficient and accurate description of the electronic structure of strongly correlated systems is still a largely unsolved problem. The usual procedures start with a multiconfigurational (usually a Complete Active Space, CAS) wavefunction which accounts for static correlation and add dynamical correlation by perturbation theory, configuration interaction, or coupled cluster expansion. This procedure requires the correct selection of the active space. Intuitive methods are unreliable for complex systems. The inexpensive black-box unrestricted natural orbital (UNO) criterion postulates that the Unrestricted Hartree-Fock (UHF) charge natural orbitals with fractional occupancy (e.g., between 0.02 and 1.98) constitute the active space. UNOs generally approximate the CAS orbitals so well that the orbital optimization in CAS Self-Consistent Field (CASSCF) may be omitted, resulting in the inexpensive UNO-CAS method. A rigorous testing of the UNO criterion requires comparison with approximate full configuration interaction wavefunctions. This became feasible with the advent of Density Matrix Renormalization Group (DMRG) methods which can approximate highly correlated wavefunctions at affordable cost. We have compared active orbital occupancies in UNO-CAS and CASSCF calculations with DMRG in a number of strongly correlated molecules: compounds of electronegative atoms (F{sub 2}, ozone, and NO{sub 2}), polyenes, aromatic molecules (naphthalene, azulene, anthracene, and nitrobenzene), radicals (phenoxy and benzyl), diradicals (o-, m-, and p-benzyne), and transition metal compounds (nickel-acetylene and Cr{sub 2}). The UNO criterion works well in these cases. Other symmetry breaking solutions, with the possible exception of spatial symmetry, do not appear to be essential to generate the correct active space. In the case of multiple UHF solutions, the natural orbitals of the average UHF density should be used. The problems of the UNO criterion and their potential solutions

  7. Selection of active spaces for multiconfigurational wavefunctions

    NASA Astrophysics Data System (ADS)

    Keller, Sebastian; Boguslawski, Katharina; Janowski, Tomasz; Reiher, Markus; Pulay, Peter

    2015-06-01

    The efficient and accurate description of the electronic structure of strongly correlated systems is still a largely unsolved problem. The usual procedures start with a multiconfigurational (usually a Complete Active Space, CAS) wavefunction which accounts for static correlation and add dynamical correlation by perturbation theory, configuration interaction, or coupled cluster expansion. This procedure requires the correct selection of the active space. Intuitive methods are unreliable for complex systems. The inexpensive black-box unrestricted natural orbital (UNO) criterion postulates that the Unrestricted Hartree-Fock (UHF) charge natural orbitals with fractional occupancy (e.g., between 0.02 and 1.98) constitute the active space. UNOs generally approximate the CAS orbitals so well that the orbital optimization in CAS Self-Consistent Field (CASSCF) may be omitted, resulting in the inexpensive UNO-CAS method. A rigorous testing of the UNO criterion requires comparison with approximate full configuration interaction wavefunctions. This became feasible with the advent of Density Matrix Renormalization Group (DMRG) methods which can approximate highly correlated wavefunctions at affordable cost. We have compared active orbital occupancies in UNO-CAS and CASSCF calculations with DMRG in a number of strongly correlated molecules: compounds of electronegative atoms (F2, ozone, and NO2), polyenes, aromatic molecules (naphthalene, azulene, anthracene, and nitrobenzene), radicals (phenoxy and benzyl), diradicals (o-, m-, and p-benzyne), and transition metal compounds (nickel-acetylene and Cr2). The UNO criterion works well in these cases. Other symmetry breaking solutions, with the possible exception of spatial symmetry, do not appear to be essential to generate the correct active space. In the case of multiple UHF solutions, the natural orbitals of the average UHF density should be used. The problems of the UNO criterion and their potential solutions are discussed

  8. Selection of active spaces for multiconfigurational wavefunctions.

    PubMed

    Keller, Sebastian; Boguslawski, Katharina; Janowski, Tomasz; Reiher, Markus; Pulay, Peter

    2015-06-28

    The efficient and accurate description of the electronic structure of strongly correlated systems is still a largely unsolved problem. The usual procedures start with a multiconfigurational (usually a Complete Active Space, CAS) wavefunction which accounts for static correlation and add dynamical correlation by perturbation theory, configuration interaction, or coupled cluster expansion. This procedure requires the correct selection of the active space. Intuitive methods are unreliable for complex systems. The inexpensive black-box unrestricted natural orbital (UNO) criterion postulates that the Unrestricted Hartree-Fock (UHF) charge natural orbitals with fractional occupancy (e.g., between 0.02 and 1.98) constitute the active space. UNOs generally approximate the CAS orbitals so well that the orbital optimization in CAS Self-Consistent Field (CASSCF) may be omitted, resulting in the inexpensive UNO-CAS method. A rigorous testing of the UNO criterion requires comparison with approximate full configuration interaction wavefunctions. This became feasible with the advent of Density Matrix Renormalization Group (DMRG) methods which can approximate highly correlated wavefunctions at affordable cost. We have compared active orbital occupancies in UNO-CAS and CASSCF calculations with DMRG in a number of strongly correlated molecules: compounds of electronegative atoms (F2, ozone, and NO2), polyenes, aromatic molecules (naphthalene, azulene, anthracene, and nitrobenzene), radicals (phenoxy and benzyl), diradicals (o-, m-, and p-benzyne), and transition metal compounds (nickel-acetylene and Cr2). The UNO criterion works well in these cases. Other symmetry breaking solutions, with the possible exception of spatial symmetry, do not appear to be essential to generate the correct active space. In the case of multiple UHF solutions, the natural orbitals of the average UHF density should be used. The problems of the UNO criterion and their potential solutions are discussed

  9. Polymer quantum mechanics some examples using path integrals

    SciTech Connect

    Parra, Lorena; Vergara, J. David

    2014-01-14

    In this work we analyze several physical systems in the context of polymer quantum mechanics using path integrals. First we introduce the group averaging method to quantize constrained systems with path integrals and later we use this procedure to compute the effective actions for the polymer non-relativistic particle and the polymer harmonic oscillator. We analyze the measure of the path integral and we describe the semiclassical dynamics of the systems.

  10. Dynamical phase transitions in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Rotter, Ingrid

    2012-02-01

    The nucleus is described as an open many-body quantum system with a non-Hermitian Hamilton operator the eigenvalues of which are complex, in general. The eigenvalues may cross in the complex plane (exceptional points), the phases of the eigenfunctions are not rigid in approaching the crossing points and the widths bifurcate. By varying only one parameter, the eigenvalue trajectories usually avoid crossing and width bifurcation occurs at the critical value of avoided crossing. An analog spectroscopic redistribution takes place for discrete states below the particle decay threshold. By this means, a dynamical phase transition occurs in the many-level system starting at a critical value of the level density. Hence the properties of the low-lying nuclear states (described well by the shell model) and those of highly excited nuclear states (described by random ensembles) differ fundamentally from one another. The statement of Niels Bohr on the collective features of compound nucleus states at high level density is therefore not in contradiction to the shell-model description of nuclear (and atomic) states at low level density. Dynamical phase transitions are observed experimentally in different quantum mechanical systems by varying one or two parameters.

  11. Quantum Mechanics and the Principle of Least Radix Economy

    NASA Astrophysics Data System (ADS)

    Garcia-Morales, Vladimir

    2015-03-01

    A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this concept in a unified way. The principle reinterprets and generalizes the principle of least action yielding two classes of physical solutions: least action paths and quantum wavefunctions. A new physical foundation of the Hilbert space of quantum mechanics is then accomplished and it is used to derive the Schrödinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new (pre-geometrical) foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann's principle of classical statistical thermodynamics. A new expression for a general (path-dependent) nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics.

  12. Quantum mechanics in fractional and other anomalous spacetimes

    SciTech Connect

    Calcagni, Gianluca; Nardelli, Giuseppe; Scalisi, Marco

    2012-10-15

    We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the wave-functions minimizing the uncertainty are found. In spite of the fact that ordinary time and spatial translations are broken and the dynamics is not unitary, the theory is in one-to-one correspondence with a unitary one, thus allowing us to employ standard tools of analysis. These features are illustrated in the examples of the free particle and the harmonic oscillator. While fractional (and the more general anomalous-spacetime) free models are formally indistinguishable from ordinary ones at the classical level, at the quantum level they differ both in the Hilbert space and for a topological term fixing the classical action in the path integral formulation. Thus, all non-unitarity in fractional quantum dynamics is encoded in a contribution depending only on the initial and final states.

  13. Multichannel framework for singular quantum mechanics

    SciTech Connect

    Camblong, Horacio E.; Epele, Luis N.; Fanchiotti, Huner; García Canal, Carlos A.; Ordóñez, Carlos R.

    2014-01-15

    A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant (“asymptotic”) observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances. -- Highlights: •A multichannel framework is proposed for singular quantum mechanics and analogues. •The framework unifies several established approaches for singular potentials. •Singular points are treated as new scattering channels. •Nonunitary asymptotic behavior is subsumed in a unitary multichannel S-matrix. •Conformal quantum mechanics and the inverse quartic potential are highlighted.

  14. The SCOP-formalism: an Operational Approach to Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    D'Hooghe, Bart

    2010-05-01

    We present the SCOP-formalism, an operational approach to quantum mechanics. If a State—COntext—Property—System (SCOP) satisfies a specific set of `quantum axioms,] it fits in a quantum mechanical representation in Hilbert space. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter N. In the case N = 2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N→∞ the system is classical. For the intermediate cases it is impossible to define an orthocomplementation on the set of properties. Another interesting feature is that the probability of a state transition also depends on the context which induces it. This contrasts sharply with standard quantum mechanics for which Gleason's theorem states the uniqueness of the state transition probability and independent of measurement context. We show that if a SCOP satisfies a Gleason-like condition, namely that all state transition probabilities are independent of which measurement context induces the change of state, then the lattice of properties is orthocomplemented.

  15. Relativistic Bohmian interpretation of quantum mechanics

    SciTech Connect

    Nikolic, Hrvoje

    2006-06-27

    I present a relativistic covariant version of the Bohmian interpretation of quantum mechanics and discuss the corresponding measurable predictions. The covariance is incoded in the fact that the nonlocal quantum potential transforms as a scalar, which is a consequence of the fact that the nonlocal wave function transforms as a scalar. The measurable predictions that can be obtained with the deterministic Bohmian interpretation cannot be obtained with the conventional interpretation simply because the conventional probabilistic interpretation does not work in the case of relativistic quantum mechanics.

  16. An Axiomatic Basis for Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Cassinelli, Gianni; Lahti, Pekka

    2016-10-01

    In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in this derivation are the co-ordinatization of generalized geometries and a theorem of Solér which characterizes Hilbert spaces among the orthomodular spaces. A generalized Wigner theorem is applied to reduce some of the assumptions of Solér's theorem to the theory of symmetry in quantum mechanics. Since this reduction is only partial we also point out the remaining open questions.

  17. An Axiomatic Basis for Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Cassinelli, Gianni; Lahti, Pekka

    2016-06-01

    In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in this derivation are the co-ordinatization of generalized geometries and a theorem of Solér which characterizes Hilbert spaces among the orthomodular spaces. A generalized Wigner theorem is applied to reduce some of the assumptions of Solér's theorem to the theory of symmetry in quantum mechanics. Since this reduction is only partial we also point out the remaining open questions.

  18. Quantum mechanics as applied mathematical statistics

    SciTech Connect

    Skala, L.; Cizek, J.; Kapsa, V.

    2011-05-15

    Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.

  19. Two basic Uncertainty Relations in Quantum Mechanics

    SciTech Connect

    Angelow, Andrey

    2011-04-07

    In the present article, we discuss two types of uncertainty relations in Quantum Mechanics-multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schroedinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics-Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.

  20. Two basic Uncertainty Relations in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Angelow, Andrey

    2011-04-01

    In the present article, we discuss two types of uncertainty relations in Quantum Mechanics-multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schrödinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics-Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.

  1. Quantum Mechanics, Pattern Recognition, and the Mammalian Brain

    NASA Astrophysics Data System (ADS)

    Chapline, George

    2008-10-01

    Although the usual way of representing Markov processes is time asymmetric, there is a way of describing Markov processes, due to Schrodinger, which is time symmetric. This observation provides a link between quantum mechanics and the layered Bayesian networks that are often used in automated pattern recognition systems. In particular, there is a striking formal similarity between quantum mechanics and a particular type of Bayesian network, the Helmholtz machine, which provides a plausible model for how the mammalian brain recognizes important environmental situations. One interesting aspect of this relationship is that the "wake-sleep" algorithm for training a Helmholtz machine is very similar to the problem of finding the potential for the multi-channel Schrodinger equation. As a practical application of this insight it may be possible to use inverse scattering techniques to study the relationship between human brain wave patterns, pattern recognition, and learning. We also comment on whether there is a relationship between quantum measurements and consciousness.

  2. A quantum mechanical polarizable force field for biomolecular interactions.

    PubMed

    Donchev, A G; Ozrin, V D; Subbotin, M V; Tarasov, O V; Tarasov, V I

    2005-05-31

    We introduce a quantum mechanical polarizable force field (QMPFF) fitted solely to QM data at the MP2/aTZ(-hp) level. Atomic charge density is modeled by point-charge nuclei and floating exponentially shaped electron clouds. The functional form of interaction energy parallels quantum mechanics by including electrostatic, exchange, induction, and dispersion terms. Separate fitting of each term to the counterpart calculated from high-quality QM data ensures high transferability of QMPFF parameters to different molecular environments, as well as accurate fit to a broad range of experimental data in both gas and liquid phases. QMPFF, which is much more efficient than ab initio QM, is optimized for the accurate simulation of biomolecular systems and the design of drugs.

  3. The geometric semantics of algebraic quantum mechanics.

    PubMed

    Cruz Morales, John Alexander; Zilber, Boris

    2015-08-01

    In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.

  4. Quantum mechanics: The subtle pull of emptiness

    SciTech Connect

    Seife, C.

    1997-01-10

    Classic physics dictates that the vacuum is devoid not only of matter but also of energy. But quantum mechanics often seems to depart from common sense. A paper in the Physical Review Letters describes the first successful measurement of the ultimate quantum free lunch: the Casimir force, a pressure exerted by empty space. This paper describes the background and the experiment.

  5. Quantum Mechanics Studies of Cellobiose Conformations

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Three regions of the Phi,Psi space of cellobiose were analyzed with quantum mechanics. A central region, in which most crystal structures are found, was covered by a 9 x 9 grid of 20° increments of Phi and Psi. Besides these 81 constrained minimizations, we studied two central sub-regions and two re...

  6. Quantum mechanics is compatible with realism

    SciTech Connect

    Burgos, M.E.

    1987-08-01

    A new paradox of quantum mechanics has recently been proposed by an author claiming that any attempt to inject realism in physical theory is bound to lead to inconsistencies. In this paper the author shows that the mentioned paradox is not such a one and that at present there are no reasons to reject realism.

  7. Conditions for nondegeneracy in supersymmetric quantum mechanics

    SciTech Connect

    Imbo, T.D.; Sukhatme, U.P.

    1986-05-15

    It is shown that the positive ''bosonic'' and ''fermionic'' bound-state spectra in spherically symmetric supersymmetric (SUSY) quantum mechanics are degenerate if and only if the superpotential W(r) satisfies deltaequivalentlim/sub r/..-->..0rVertical BarW(r)Vertical Bar> or =0.5. Also, if delta<0.5, then SUSY is broken.

  8. Subjective and objective probabilities in quantum mechanics

    SciTech Connect

    Srednicki, Mark

    2005-05-15

    We discuss how the apparently objective probabilities predicted by quantum mechanics can be treated in the framework of Bayesian probability theory, in which all probabilities are subjective. Our results are in accord with earlier work by Caves, Fuchs, and Schack, but our approach and emphasis are different. We also discuss the problem of choosing a noninformative prior for a density matrix.

  9. Comparison of Classical and Quantum Mechanical Uncertainties.

    ERIC Educational Resources Information Center

    Peslak, John, Jr.

    1979-01-01

    Comparisons are made for the particle-in-a-box, the harmonic oscillator, and the one-electron atom. A classical uncertainty principle is derived and compared with its quantum-mechanical counterpart. The results are discussed in terms of the statistical interpretation of the uncertainty principle. (Author/BB)

  10. Quantum mechanics and the generalized uncertainty principle

    SciTech Connect

    Bang, Jang Young; Berger, Micheal S.

    2006-12-15

    The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.

  11. A Reconstruction of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Kochen, Simon

    2015-05-01

    We show that exactly the same intuitively plausible definitions of state, observable, symmetry, dynamics, and compound systems of the classical Boolean structure of intrinsic properties of systems lead, when applied to the structure of extrinsic, relational quantum properties, to the standard quantum formalism, including the Schrödinger equation and the von Neumann-Lüders Projection Rule. This approach is then applied to resolving the paradoxes and difficulties of the orthodox interpretation.

  12. On factorization of molecular wavefunctions

    NASA Astrophysics Data System (ADS)

    Jecko, Thierry; Sutcliffe, Brian T.; Woolley, R. Guy

    2015-11-01

    Recently there has been a renewed interest in the chemical physics literature of factorization of the position representation eigenfunctions Φ of the molecular Schrödinger equation as originally proposed by Hunter in the 1970s. The idea is to represent Φ in the form φχ where χ is purely a function of the nuclear coordinates, while φ must depend on both electron and nuclear position variables in the problem. This is a generalization of the approximate factorization originally proposed by Born and Oppenheimer, the hope being that an ‘exact’ representation of Φ can be achieved in this form with φ and χ interpretable as ‘electronic’ and ‘nuclear’ wavefunctions respectively. We offer a mathematical analysis of these proposals that identifies ambiguities stemming mainly from the singularities in the Coulomb potential energy.

  13. Effects of a scalar scaling field on quantum mechanics

    NASA Astrophysics Data System (ADS)

    Benioff, Paul

    2016-07-01

    This paper describes the effects of a complex scalar scaling field on quantum mechanics. The field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field. The extension is based on the idea that the value of a number at one space time point does not determine the value at another point. This, combined with the description of mathematical systems as structures of different types, results in the presence of separate number fields and vector spaces as structures, at different space time locations. Complex number structures and vector spaces at each location are scaled by a complex space time dependent scaling factor. The effect of this scaling factor on several physical and geometric quantities has been described in other work. Here the emphasis is on quantum mechanics of one and two particles, their states and properties. Multiparticle states are also briefly described. The effect shows as a complex, nonunitary, scalar field connection on a fiber bundle description of nonrelativistic quantum mechanics. The lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small. It also means that the gradient of the field must be very small in a local region of cosmological space and time. Outside this region, there are no restrictions on the field gradient.

  14. Novel symmetries in N=2 supersymmetric quantum mechanical models

    SciTech Connect

    Malik, R.P.; Khare, Avinash

    2013-07-15

    We demonstrate the existence of a novel set of discrete symmetries in the context of the N=2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the X–Y plane under the influence of a magnetic field in the Z-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We show that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary N=2 SUSY quantum mechanical system can be shown to be a tractable model for the Hodge theory. -- Highlights: •Discrete symmetries of two completely different kinds of N=2 supersymmetric quantum mechanical models have been discussed. •The discrete symmetries provide physical realizations of Hodge duality. •The continuous symmetries provide the physical realizations of de Rham cohomological operators. •Our work sheds a new light on the meaning of the above abstract operators.

  15. A Separable, Dynamically Local Ontological Model of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Pienaar, Jacques

    2016-01-01

    A model of reality is called separable if the state of a composite system is equal to the union of the states of its parts, located in different regions of space. Spekkens has argued that it is trivial to reproduce the predictions of quantum mechanics using a separable ontological model, provided one allows for arbitrary violations of `dynamical locality'. However, since dynamical locality is strictly weaker than local causality, this leaves open the question of whether an ontological model for quantum mechanics can be both separable and dynamically local. We answer this question in the affirmative, using an ontological model based on previous work by Deutsch and Hayden. Although the original formulation of the model avoids Bell's theorem by denying that measurements result in single, definite outcomes, we show that the model can alternatively be cast in the framework of ontological models, where Bell's theorem does apply. We find that the resulting model violates local causality, but satisfies both separability and dynamical locality, making it a candidate for the `most local' ontological model of quantum mechanics.

  16. Quantum mechanical evolution operator in the presence of a scalar linear potential: discussion on the evolved state, phase shift generator and tunneling

    NASA Astrophysics Data System (ADS)

    Fratini, F.; Safari, L.

    2014-08-01

    We discuss the form of the wave-function of a state subjected to a scalar linear potential, focusing on quantum tunneling. We analyze the phases acquired by the evolved state and show that some are of a pure quantum mechanical origin. We propose a simple experimental scenario to measure one of these phases. We apply the evolution equations to re-analyze the Stern and Gerlach experiment and to demonstrate how to manipulate spin by employing constant electric fields.

  17. Review of the inverse scattering problem at fixed energy in quantum mechanics

    NASA Technical Reports Server (NTRS)

    Sabatier, P. C.

    1972-01-01

    Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.

  18. Consistent interpretations of quantum mechanics

    SciTech Connect

    Omnes, R. )

    1992-04-01

    Within the last decade, significant progress has been made towards a consistent and complete reformulation of the Copenhagen interpretation (an interpretation consisting in a formulation of the experimental aspects of physics in terms of the basic formalism; it is consistent if free from internal contradiction and complete if it provides precise predictions for all experiments). The main steps involved decoherence (the transition from linear superpositions of macroscopic states to a mixing), Griffiths histories describing the evolution of quantum properties, a convenient logical structure for dealing with histories, and also some progress in semiclassical physics, which was made possible by new methods. The main outcome is a theory of phenomena, viz., the classically meaningful properties of a macroscopic system. It shows in particular how and when determinism is valid. This theory can be used to give a deductive form to measurement theory, which now covers some cases that were initially devised as counterexamples against the Copenhagen interpretation. These theories are described, together with their applications to some key experiments and some of their consequences concerning epistemology.

  19. Uncertainty in quantum mechanics: faith or fantasy?

    PubMed

    Penrose, Roger

    2011-12-13

    The word 'uncertainty', in the context of quantum mechanics, usually evokes an impression of an essential unknowability of what might actually be going on at the quantum level of activity, as is made explicit in Heisenberg's uncertainty principle, and in the fact that the theory normally provides only probabilities for the results of quantum measurement. These issues limit our ultimate understanding of the behaviour of things, if we take quantum mechanics to represent an absolute truth. But they do not cause us to put that very 'truth' into question. This article addresses the issue of quantum 'uncertainty' from a different perspective, raising the question of whether this term might be applied to the theory itself, despite its unrefuted huge success over an enormously diverse range of observed phenomena. There are, indeed, seeming internal contradictions in the theory that lead us to infer that a total faith in it at all levels of scale leads us to almost fantastical implications.

  20. Quantum Mechanics, Gravity, and the Multiverse

    NASA Astrophysics Data System (ADS)

    Nomura, Yasunori

    2012-04-01

    The discovery of accelerating expansion of the universe has led us to take the dramatic view that our universe may be one of the many universes in which low energy physical laws take different forms: the multiverse. I explain why/how this view is supported both observationally and theoretically, especially by string theory and eternal inflation. I then describe how quantum mechanics plays a crucial role in understanding the multiverse, even at the largest distance scales. The resulting picture leads to a revolutionary change of our view of spacetime and gravity, and completely unifies the paradigm of the eternally inflating multiverse with the many worlds interpretation of quantum mechanics. The picture also provides a solution to a long-standing problem in eternal inflation, called the measure problem, which I briefly describe.

  1. Beyond relativity and quantum mechanics: space physics

    NASA Astrophysics Data System (ADS)

    Lindner, Henry H.

    2011-09-01

    Albert Einstein imposed an observer-based epistemology upon physics. Relativity and Quantum Mechanics limit physics to describing and modeling the observer's sensations and measurements. Their "underlying reality" consists only of ideas that serve to model the observer's experience. These positivistic models cannot be used to form physical theories of Cosmic phenomena. To do this, we must again remove the observer from the center of physics. When we relate motion to Cosmic space instead of to observers and we attempt to explain the causes of Cosmic phenomena, we are forced to admit that Cosmic space is a substance. We need a new physics of space. We can begin by replacing Relativity with a modified Lorentzian-Newtonian model of spatial flow, and Quantum Mechanics with a wave-based theory of light and electrons. Space physics will require the reinterpretation of all known phenomena, concepts, and mathematical models.

  2. Measurements and mathematical formalism of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Slavnov, D. A.

    2007-03-01

    A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantum mechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.

  3. Covariant quantum mechanics applied to noncommutative geometry

    NASA Astrophysics Data System (ADS)

    Astuti, Valerio

    2015-08-01

    We here report a result obtained in collaboration with Giovanni Amelino-Camelia, first shown in the paper [1]. Applying the manifestly covariant formalism of quantum mechanics to the much studied Snyder spacetime [2] we show how it is trivial in every physical observables, this meaning that every measure in this spacetime gives the same results that would be obtained in the flat Minkowski spacetime.

  4. A Philosopher's Understanding of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Vermaas, Pieter E.

    2005-07-01

    1. Introduction; 2. Quantum mechanics; 3. Modal interpretations; Part I. Formalism: 4. The different versions; 5. The full property ascription; 6. Joint property ascriptions; 7. Discontinuities, instabilities and other bad behaviour; 8. Transition probabilities; 9. Dynamical autonomy and locality; Part II. Physics: 10. The measurement problem; 11. The Born rule; Part III. Philosophy: 12. Properties, states, measurement outcomes and effective states; 13. Holism versus reductionism; 14. Possibilities and impossibilities; 15. Conclusions.

  5. A Philosopher's Understanding of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Vermaas, Pieter E.

    2000-02-01

    1. Introduction; 2. Quantum mechanics; 3. Modal interpretations; Part I. Formalism: 4. The different versions; 5. The full property ascription; 6. Joint property ascriptions; 7. Discontinuities, instabilities and other bad behaviour; 8. Transition probabilities; 9. Dynamical autonomy and locality; Part II. Physics: 10. The measurement problem; 11. The Born rule; Part III. Philosophy: 12. Properties, states, measurement outcomes and effective states; 13. Holism versus reductionism; 14. Possibilities and impossibilities; 15. Conclusions.

  6. Coherent states in noncommutative quantum mechanics

    SciTech Connect

    Ben Geloun, J.; Scholtz, F. G.

    2009-04-15

    Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position uncertainty relation, obey a Poisson distribution, and possess a flat geometry. Using the natural isometry between the quantum Hilbert space of Hilbert-Schmidt operators and the tensor product of the classical configuration space and its dual, we reveal the inherent vector feature of these states.

  7. Strange Bedfellows: Quantum Mechanics and Data Mining

    SciTech Connect

    Weinstein, Marvin; /SLAC

    2009-12-16

    Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.

  8. Time in classical and in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Elçi, A.

    2010-07-01

    This paper presents an analysis of the time concept in classical mechanics from the perspective of the invariants of a motion. The analysis shows that there is a conceptual gap concerning time in the Dirac-Heisenberg-von Neumann formalism and that Bohr's complementarity principle does not fill the gap. In the Dirac-Heisenberg-von Neumann formalism, a particle's properties are represented by Heisenberg matrices. This axiom is the source of the time problem in quantum mechanics.

  9. Quantum mechanics lessons for standard cosmology

    NASA Astrophysics Data System (ADS)

    Reyes, Marco A.

    2012-08-01

    By recalling the relevance of the Sturm-Liouville theory has had on the solutions of quantum mechanics problems, here it is explored the possibility of getting some insight to the solutions for a standard cosmology model for inflation, from a time independent Schrödinger type equation derived from the equations of motion for a single scalar field in a flat space time with a FRW metric and a cosmological constant.

  10. Collocation method for fractional quantum mechanics

    SciTech Connect

    Amore, Paolo; Hofmann, Christoph P.; Saenz, Ricardo A.; Fernandez, Francisco M.

    2010-12-15

    We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on little sinc functions, which discretizes the Schroedinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a Wentzel-Kramers-Brillouin analysis is performed.

  11. How to Teach the Postulates of Quantum Mechanics without Enigma.

    ERIC Educational Resources Information Center

    Teixeira-Dias, Jose J. C.

    1983-01-01

    Shows how a statistical approach can help students accept postulates of quantum mechanics. The approach, which also makes students aware of the philosophical/humanistic implications of quantum mechanics, involves the following sequence: (1) important experiments in quantum mechanics; (2) conventional statistical interpretation; (3) mathematical…

  12. Improving students' understanding of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Singh, Chandralekha

    2011-03-01

    Learning quantum mechanics is especially challenging, in part due to the abstract nature of the subject. We have been conducting investigations of the difficulties that students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) as well as tools for peer-instruction. The goal of QuILTs and peer-instruction tools is to actively engage students in the learning process and to help them build links between the formalism and the conceptual aspects of quantum physics without compromising the technical content. They focus on helping students integrate qualitative and quantitative understanding, confront and resolve their misconceptions and difficulties, and discriminate between concepts that are often confused. In this talk, I will give examples from my research in physics education of how students' prior knowledge relevant for quantum mechanics can be assessed, and how learning tools can be designed to help students develop a robust knowledge structure and critical thinking skills. Supported by the National Science Foundation.

  13. Some reflections on the role of semi-classical atomic models in the teaching and learning of introductory quantum mechanics

    NASA Astrophysics Data System (ADS)

    O'Sullivan, Colm

    2016-03-01

    The role of "semi-classical" (Bohr-Sommerfeld) and "semi-quantum-mechanical" (atomic orbital) models in the context of the teaching of atomic theory is considered. It is suggested that an appropriate treatment of such models can serve as a useful adjunct to quantum mechanical study of atomic systems.

  14. Jarzynski Equality in PT-Symmetric Quantum Mechanics.

    PubMed

    Deffner, Sebastian; Saxena, Avadh

    2015-04-17

    We show that the quantum Jarzynski equality generalizes to PT-symmetric quantum mechanics with unbroken PT symmetry. In the regime of broken PT symmetry, the Jarzynski equality does not hold as also the CPT norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system-two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken PT symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.

  15. Multiscale quantum mechanics/electromagnetics simulation for electronic devices.

    PubMed

    Yam, ChiYung; Meng, Lingyi; Chen, GuanHua; Chen, Quan; Wong, Ngai

    2011-08-28

    The continuous downsizing of modern electronic devices implies the increasing importance of quantum phenomena. As the feature sizes of transistors inch towards 10 nanometer, simulations including quantum effects and atomistic details are inevitable. Here we report a novel hybrid quantum mechanics and electromagnetics (QM/EM) method to model individual electronic components at the nanoscale. QM and EM models are solved in different regions of the system in a self-consistent manner. As a demonstration, we study a carbon nanotube based electronic device embedded in a silicon block. Good agreement is obtained between simulation by QM/EM method and full QM treatment of the entire system.

  16. Sine-square deformation and supersymmetric quantum mechanics

    NASA Astrophysics Data System (ADS)

    Okunishi, Kouichi; Katsura, Hosho

    2015-11-01

    We investigate the sine-square deformation (SSD) of free fermions in one-dimensional continuous space. On the basis of supersymmetric quantum mechanics, we prove the correspondence between the many-body ground state of the system with SSD and that of the uniform system with periodic boundary conditions. We also discuss the connection between the SSD in the continuous space and its lattice version, where the geometric correction due to the real-space deformation plays an important role in relating the eigenstates of the lattice SSD with those of the continuous SSD.

  17. Use of mathematical logical concepts in quantum mechanics: an example

    NASA Astrophysics Data System (ADS)

    Benioff, Paul

    2002-07-01

    The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has meaning. A simple example of such a system, based on an example described by Smullyan, is studied here. Based on a path interpretation for some word states, definitions of truth, validity, consistency and completeness are given and their properties studied. It is also shown that the relation between the potential meaning, if any, of word states and the quantum algorithmic complexity of the process generating the word states must be quite complex or nonexistent.

  18. A proposed optical test for Popper's challenge to quantum mechanics

    NASA Astrophysics Data System (ADS)

    Reintjes, J.; Bashkansky, Mark

    2016-05-01

    We describe an optical configuration that is predicted to exhibit the behavior described by Popper in his challenge to conventional quantum mechanics. Popper rejected this behavior on the grounds that it was unphysical because it relied on observer knowledge as a causative agent. We offer an interpretation in which the behavior arises simply out of the mode properties of an entangled system. In this interpretation the observer knowledge reveals in which mode an excitation occurs, but does not affect future behavior as asserted by Popper. We also discuss the relation of our system to the quantum eraser.

  19. Jarzynski equality in PT-symmetric quantum mechanics

    SciTech Connect

    Deffner, Sebastian; Saxena, Avadh

    2015-04-13

    We show that the quantum Jarzynski equality generalizes to PT -symmetric quantum mechanics with unbroken PT -symmetry. In the regime of broken PT -symmetry the Jarzynski equality does not hold as also the CPT -norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system – two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken PT -symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.

  20. Quantum mechanical calculations of vibrational population inversion in chemical reactions - Numerically exact L-squared-amplitude-density study of the H2Br reactive system

    NASA Technical Reports Server (NTRS)

    Zhang, Y. C.; Zhang, J. Z. H.; Kouri, D. J.; Haug, K.; Schwenke, D. W.

    1988-01-01

    Numerically exact, fully three-dimensional quantum mechanicl reactive scattering calculations are reported for the H2Br system. Both the exchange (H + H-prime Br to H-prime + HBr) and abstraction (H + HBR to H2 + Br) reaction channels are included in the calculations. The present results are the first completely converged three-dimensional quantum calculations for a system involving a highly exoergic reaction channel (the abstraction process). It is found that the production of vibrationally hot H2 in the abstraction reaction, and hence the extent of population inversion in the products, is a sensitive function of initial HBr rotational state and collision energy.

  1. Models on the boundary between classical and quantum mechanics.

    PubMed

    Hooft, Gerard 't

    2015-08-01

    Arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there cannot be physical laws that require 'conspiracy'. It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In this report, several such counterexamples are shown. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. So now the question is asked: how can such a model feature 'conspiracy', and how bad is that? Is there conspiracy in the vacuum fluctuations? Arguments concerning Bell's theorem are further sharpened.

  2. Efficient hybrid-symbolic methods for quantum mechanical calculations

    NASA Astrophysics Data System (ADS)

    Scott, T. C.; Zhang, Wenxing

    2015-06-01

    We present hybrid symbolic-numerical tools to generate optimized numerical code for rapid prototyping and fast numerical computation starting from a computer algebra system (CAS) and tailored to any given quantum mechanical problem. Although a major focus concerns the quantum chemistry methods of H. Nakatsuji which has yielded successful and very accurate eigensolutions for small atoms and molecules, the tools are general and may be applied to any basis set calculation with a variational principle applied to its linear and non-linear parameters.

  3. Models on the boundary between classical and quantum mechanics.

    PubMed

    Hooft, Gerard 't

    2015-08-01

    Arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there cannot be physical laws that require 'conspiracy'. It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In this report, several such counterexamples are shown. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. So now the question is asked: how can such a model feature 'conspiracy', and how bad is that? Is there conspiracy in the vacuum fluctuations? Arguments concerning Bell's theorem are further sharpened. PMID:26124246

  4. Metric space formulation of quantum mechanical conservation laws

    NASA Astrophysics Data System (ADS)

    Sharp, P. M.; D'Amico, I.

    2014-03-01

    We show that conservation laws in quantum mechanics naturally lead to metric spaces for the set of related physical quantities. All such metric spaces have an "onion-shell" geometry. We demonstrate the power of this approach by considering many-body systems immersed in a magnetic field, with a finite ground state current. In the associated metric spaces we find regions of allowed and forbidden distances, a "band structure" in metric space directly arising from the conservation of the z component of the angular momentum.

  5. Foundation of quantum mechanics from the principle of relativity

    SciTech Connect

    Nottale, Laurent

    2007-04-28

    We briefly recall the main steps by which we suggest to found quantum mechanics and gauge field theories on the principle of relativity, once it is extended to scale transformations of the reference system. The wave functions are constructed as consequences of the nondifferentiability of a continuous space-time, while the Schroedinger and Dirac equations are obtained from its geodesics equations. In this framework, the gauge fields emerge as manifestation of the fractal geometry, and the gauge charges as the conservative quantities which are built from its internal symmetries.

  6. Quantum mechanical studies of carbon structures

    SciTech Connect

    Bartelt, Norman Charles; Ward, Donald; Zhou, Xiaowang; Foster, Michael E.; Schultz, Peter A.; Wang, Bryan M.; McCarty, Kevin F.

    2015-10-01

    Carbon nanostructures, such as nanotubes and graphene, are of considerable interest due to their unique mechanical and electrical properties. The materials exhibit extremely high strength and conductivity when defects created during synthesis are minimized. Atomistic modeling is one technique for high resolution studies of defect formation and mitigation. To enable simulations of the mechanical behavior and growth mechanisms of C nanostructures, a high-fidelity analytical bond-order potential for the C is needed. To generate inputs for developing such a potential, we performed quantum mechanical calculations of various C structures.

  7. Landau problem in noncommutative quantum mechanics

    NASA Astrophysics Data System (ADS)

    Sayipjamal, Dulat; Li, Kang

    2008-02-01

    The Landau problem in non-commutative quantum mechanics (NCQM) is studied. First by solving the Schrödinger equations on noncommutative (NC) space we obtain the Landau energy levels and the energy correction that is caused by space-space noncommutativity. Then we discuss the noncommutative phase space case, namely, space-space and momentum-momentum non-commutative case, and we get the explicit expression of the Hamiltonian as well as the corresponding eigenfunctions and eigenvalues. Supported by National Natural Science Foundation of China (10465004, 10665001, 10575026) and Abdus Salam ICTP, Trieste, Italy

  8. Multichannel framework for singular quantum mechanics

    NASA Astrophysics Data System (ADS)

    Camblong, Horacio E.; Epele, Luis N.; Fanchiotti, Huner; García Canal, Carlos A.; Ordóñez, Carlos R.

    2014-01-01

    A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant ("asymptotic") observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances.

  9. Generalized coherent states under deformed quantum mechanics with maximum momentum

    NASA Astrophysics Data System (ADS)

    Ching, Chee Leong; Ng, Wei Khim

    2013-10-01

    Following the Gazeau-Klauder approach, we construct generalized coherent states (GCS) as the quantum simulator to examine the deformed quantum mechanics, which exhibits an intrinsic maximum momentum. We study deformed harmonic oscillators and compute their probability distribution and entropy of states exactly. Also, a particle in an infinite potential box is studied perturbatively. In particular, unlike usual quantum mechanics, the present deformed case increases the entropy of the Planck scale quantum optical system. Furthermore, for simplicity, we obtain the modified uncertainty principle (MUP) with the perturbative treatment up to leading order. MUP turns out to increase generally. However, for certain values of γ (a parameter of GCS), it is possible that the MUP will vanish and hence will exhibit the classical characteristic. This is interpreted as the manifestation of the intrinsic high-momentum cutoff at lower momentum in a perturbative treatment. Although the GCS saturates the minimal uncertainty in a simultaneous measurement of physical position and momentum operators, thus constituting the squeezed states, complete coherency is impossible in quantum gravitational physics. The Mandel Q number is calculated, and it is shown that the statistics can be Poissonian and super-/sub-Poissonian depending on γ. The equation of motion is studied, and both Ehrenfest’s theorem and the correspondence principle are recovered. Fractional revival times are obtained through the autocorrelation, and they indicate that the superposition of a classical-like subwave packet is natural in GCS. We also contrast our results with the string-motivated (Snyder) type of deformed quantum mechanics, which incorporates a minimum position uncertainty rather than a maximum momentum. With the advances of quantum optics technology, it might be possible to realize some of these distinguishing quantum-gravitational features within the domain of future experiments.

  10. Entangled quantum electronic wavefunctions of the Mn4CaO5 cluster in photosystem II

    NASA Astrophysics Data System (ADS)

    Kurashige, Yuki; Chan, Garnet Kin-Lic; Yanai, Takeshi

    2013-08-01

    It is a long-standing goal to understand the reaction mechanisms of catalytic metalloenzymes at an entangled many-electron level, but this is hampered by the exponential complexity of quantum mechanics. Here, by exploiting the special structure of physical quantum states and using the density matrix renormalization group, we compute near-exact many-electron wavefunctions of the Mn4CaO5 cluster of photosystem II, with more than 1 × 1018 quantum degrees of freedom. This is the first treatment of photosystem II beyond the single-electron picture of density functional theory. Our calculations support recent modifications to the structure determined by X-ray crystallography. We further identify multiple low-lying energy surfaces associated with the structural distortion seen using X-ray crystallography, highlighting multistate reactivity in the chemistry of the cluster. Direct determination of Mn spin-projections from our wavefunctions suggests that current candidates that have been recently distinguished using parameterized spin models should be reassessed. Through entanglement maps, we reveal rich information contained in the wavefunctions on bonding changes in the cycle.

  11. Entangled quantum electronic wavefunctions of the Mn₄CaO₅ cluster in photosystem II.

    PubMed

    Kurashige, Yuki; Chan, Garnet Kin-Lic; Yanai, Takeshi

    2013-08-01

    It is a long-standing goal to understand the reaction mechanisms of catalytic metalloenzymes at an entangled many-electron level, but this is hampered by the exponential complexity of quantum mechanics. Here, by exploiting the special structure of physical quantum states and using the density matrix renormalization group, we compute near-exact many-electron wavefunctions of the Mn4CaO5 cluster of photosystem II, with more than 1 × 10(18) quantum degrees of freedom. This is the first treatment of photosystem II beyond the single-electron picture of density functional theory. Our calculations support recent modifications to the structure determined by X-ray crystallography. We further identify multiple low-lying energy surfaces associated with the structural distortion seen using X-ray crystallography, highlighting multistate reactivity in the chemistry of the cluster. Direct determination of Mn spin-projections from our wavefunctions suggests that current candidates that have been recently distinguished using parameterized spin models should be reassessed. Through entanglement maps, we reveal rich information contained in the wavefunctions on bonding changes in the cycle. PMID:23881496

  12. Time and the foundations of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Pashby, Thomas

    Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain kinds of `time observables' to find a representation within quantum theory, including clock operators (which provide the means to measure the passage of time) and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on re ection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantum mechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack.

  13. The Compton effect: Transition to quantum mechanics

    NASA Astrophysics Data System (ADS)

    Stuewer, R. H.

    2000-11-01

    The discovery of the Compton effect at the end of 1922 was a decisive event in the transition to the new quantum mechanics of 1925-1926 because it stimulated physicists to examine anew the fundamental problem of the interaction between radiation and matter. I first discuss Albert Einstein's light-quantum hypothesis of 1905 and why physicists greeted it with extreme skepticism, despite Robert A. Millikan's confirmation of Einstein's equation of the photoelectric effect in 1915. I then follow in some detail the experimental and theoretical research program that Arthur Holly Compton pursued between 1916 and 1922 at the University of Minnesota, the Westinghouse Lamp Company, the Cavendish Laboratory, and Washington University that culminated in his discovery of the Compton effect. Surprisingly, Compton was not influenced directly by Einstein's light-quantum hypothesis, in contrast to Peter Debye and H.A. Kramers, who discovered the quantum theory of scattering independently. I close by discussing the most significant response to that discovery, the Bohr-Kramers-Slater theory of 1924, its experimental refutation, and its influence on the emerging new quantum mechanics.

  14. Time of arrival in quantum mechanics

    SciTech Connect

    Grot, N.; Rovelli, C.; Tate, R.S.

    1996-12-01

    We study the problem of computing the probability for the time of arrival of a quantum particle at a given spatial position. We consider a solution to this problem based on the spectral decomposition of the particle{close_quote}s (Heisenberg) state into the eigenstates of a suitable operator, which we denote as the {open_quote}{open_quote}time-of-arrival{close_quote}{close_quote} operator. We discuss the general properties of this operator. We construct the operator explicitly in the simple case of a free nonrelativistic particle and compare the probabilities it yields with the ones estimated indirectly in terms of the flux of the Schr{umlt o}dinger current. We derive a well-defined uncertainty relation between time of arrival and energy; this result shows that the well-known arguments against the existence of such a relation can be circumvented. Finally, we define a {open_quote}{open_quote}time representation{close_quote}{close_quote} of the quantum mechanics of a free particle, in which the time of arrival is diagonal. Our results suggest that, contrary to what is commonly assumed, quantum mechanics exhibits a hidden equivalence between independent (time) and dependent (position) variables, analogous to the one revealed by the parametrized formalism in classical mechanics. {copyright} {ital 1996 The American Physical Society.}

  15. Quantum mechanics with coordinate dependent noncommutativity

    SciTech Connect

    Kupriyanov, V. G.

    2013-11-15

    Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.

  16. Differentiability of correlations in realistic quantum mechanics

    SciTech Connect

    Cabrera, Alejandro; Faria, Edson de; Pujals, Enrique; Tresser, Charles

    2015-09-15

    We prove a version of Bell’s theorem in which the locality assumption is weakened. We start by assuming theoretical quantum mechanics and weak forms of relativistic causality and of realism (essentially the fact that observable values are well defined independently of whether or not they are measured). Under these hypotheses, we show that only one of the correlation functions that can be formulated in the framework of the usual Bell theorem is unknown. We prove that this unknown function must be differentiable at certain angular configuration points that include the origin. We also prove that, if this correlation is assumed to be twice differentiable at the origin, then we arrive at a version of Bell’s theorem. On the one hand, we are showing that any realistic theory of quantum mechanics which incorporates the kinematic aspects of relativity must lead to this type of rough correlation function that is once but not twice differentiable. On the other hand, this study brings us a single degree of differentiability away from a relativistic von Neumann no hidden variables theorem.

  17. An approach to nonstandard quantum mechanics

    NASA Astrophysics Data System (ADS)

    Raab, A.

    2004-12-01

    We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to nonrelativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the Mo/ller wave operators and the S-matrix.

  18. Comment on ``Arrival time in quantum mechanics'' and ``Time of arrival in quantum mechanics''

    NASA Astrophysics Data System (ADS)

    Kijowski, Jerzy

    1999-01-01

    Contrary to claims contained in papers by Grot, Rovelli, and Tate [Phys. Rev. A 54, 4676 1996)] and Delgado and Muga [Phys. Rev. A 56, 3425 (1997)], the ``time operator,'' which I have constructed [Rep. Math. Phys. 6, 361 (1974)] in an axiomatic way, is a self-adjoint operator existing in a usual Hilbert space of (nonrelativistic or relativistic) quantum mechanics.

  19. Multiple-event probability in general-relativistic quantum mechanics

    SciTech Connect

    Hellmann, Frank; Mondragon, Mauricio; Perez, Alejandro; Rovelli, Carlo

    2007-04-15

    We discuss the definition of quantum probability in the context of 'timeless' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the 'wave function collapse' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse.

  20. Supersymmetric quantum mechanics and the Korteweg--de Vries hierarchy

    SciTech Connect

    Grant, A.K.; Rosner, J.L. )

    1994-05-01

    The connection between supersymmetric quantum mechanics and the Korteweg--de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the [tau] function by means of supersymmetric quantum mechanics is discussed.

  1. A dynamical time operator in Dirac's relativistic quantum mechanics

    NASA Astrophysics Data System (ADS)

    Bauer, M.

    2014-03-01

    A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The ensuing time-energy uncertainty relation involves the uncertainty in the instant of time when the wave packet passes a particular spatial position and the energy uncertainty associated with the wave packet at the same time, as envisaged originally by Bohr. The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in electron channeling, in interference in time, in Zitterbewegung-like effects in spintronics, graphene and superconducting systems and in cosmology is noted.

  2. Answering Dirac's Challenge: Practical Quantum Mechanics for Materials

    NASA Astrophysics Data System (ADS)

    Chelikowsky, James

    2012-10-01

    Over eight decades ago, after the invention of quantum mechanics, P. A. M. Dirac made the following observation: ``The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems...'' The creation of ``approximate practical methods'' in response to Dirac's challenge has included the one electron picture, density functional theory and the pseudopotential concept. The combination of such methods in conjunction with contemporary computational platforms and new algorithms offer the possibility of predicting properties of materials solely on the basis of the atomic species present. I will give an overview of progress in this field with an emphasis on materials at the nanoscale.

  3. Efficient quantum trajectory representation of wavefunctions evolving in imaginary time

    SciTech Connect

    Garashchuk, Sophya; Mazzuca, James; Vazhappilly, Tijo

    2011-07-21

    The Boltzmann evolution of a wavefunction can be recast as imaginary-time dynamics of the quantum trajectory ensemble. The quantum effects arise from the momentum-dependent quantum potential - computed approximately to be practical in high-dimensional systems - influencing the trajectories in addition to the external classical potential [S. Garashchuk, J. Chem. Phys. 132, 014112 (2010)]. For a nodeless wavefunction represented as {psi}(x, t) = exp ( -S(x, t)/({Dirac_h}/2{pi})) with the trajectory momenta defined by {nabla}S(x, t), analysis of the Lagrangian and Eulerian evolution shows that for bound potentials the former is more accurate while the latter is more practical because the Lagrangian quantum trajectories diverge with time. Introduction of stationary and time-dependent components into the wavefunction representation generates new Lagrangian-type dynamics where the trajectory spreading is controlled improving efficiency of the trajectory description. As an illustration, different types of dynamics are used to compute zero-point energy of a strongly anharmonic well and low-lying eigenstates of a high-dimensional coupled harmonic system.

  4. Retrocausal quantum mechanics: Maudlin's challenge revisited

    NASA Astrophysics Data System (ADS)

    Lewis, Peter J.

    2013-11-01

    In 1994, Maudlin proposed an objection to retrocausal approaches to quantum mechanics in general, and to the transactional interpretation (TI) in particular, involving an absorber that changes location depending on the trajectory of the particle. Maudlin considered this objection fatal. However, the TI did not die; rather, a number of responses were developed, some attempting to accommodate Maudlin's example within the existing TI, and others modifying the TI. I argue that none of these responses is fully adequate. The reason, I submit, is that there are two aspects to Maudlin's objection; the more readily soluble aspect has received all the attention, but the more problematic aspect has gone unnoticed. I consider the prospects for developing a successful retrocausal quantum theory in light of this second aspect of the objection.

  5. Can quantum mechanics fool the cosmic censor?

    SciTech Connect

    Matsas, G. E. A.; Silva, A. R. R. da; Richartz, M.; Saa, A.; Vanzella, D. A. T.

    2009-05-15

    We revisit the mechanism for violating the weak cosmic-censorship conjecture (WCCC) by overspinning a nearly-extreme charged black hole. The mechanism consists of an incoming massless neutral scalar particle, with low energy and large angular momentum, tunneling into the hole. We investigate the effect of the large angular momentum of the incoming particle on the background geometry and address recent claims that such a backreaction would invalidate the mechanism. We show that the large angular momentum of the incident particle does not constitute an obvious impediment to the success of the overspinning quantum mechanism, although the induced backreaction turns out to be essential to restoring the validity of the WCCC in the classical regime. These results seem to endorse the view that the 'cosmic censor' may be oblivious to processes involving quantum effects.

  6. Waveform information from quantum mechanical entropy

    NASA Astrophysics Data System (ADS)

    Funkhouser, Scott; Suski, William; Winn, Andrew

    2016-06-01

    Although the entropy of a given signal-type waveform is technically zero, it is nonetheless desirable to use entropic measures to quantify the associated information. Several such prescriptions have been advanced in the literature but none are generally successful. Here, we report that the Fourier-conjugated `total entropy' associated with quantum-mechanical probabilistic amplitude functions (PAFs) is a meaningful measure of information in non-probabilistic real waveforms, with either the waveform itself or its (normalized) analytic representation acting in the role of the PAF. Detailed numerical calculations are presented for both adaptations, showing the expected informatic behaviours in a variety of rudimentary scenarios. Particularly noteworthy are the sensitivity to the degree of randomness in a sequence of pulses and potential for detection of weak signals.

  7. Gauge invariance and reciprocity in quantum mechanics

    SciTech Connect

    Leung, P. T.; Young, K.

    2010-03-15

    Reciprocity in wave propagation usually refers to the symmetry of the Green's function under the interchange of the source and the observer coordinates, but this condition is not gauge invariant in quantum mechanics, a problem that is particularly significant in the presence of a vector potential. Several possible alternative criteria are given and analyzed with reference to different examples with nonzero magnetic fields and/or vector potentials, including the case of a multiply connected spatial domain. It is shown that the appropriate reciprocity criterion allows for specific phase factors separable into functions of the source and observer coordinates and that this condition is robust with respect to the addition of any scalar potential. In the Aharonov-Bohm effect, reciprocity beyond monoenergetic experiments holds only because of subsidiary conditions satisfied in actual experiments: the test charge is in units of e and the flux is produced by a condensate of particles with charge 2e.

  8. Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

    PubMed

    Chou, Chia-Chun; Kouri, Donald J

    2013-04-25

    We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.

  9. Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

    PubMed

    Chou, Chia-Chun; Kouri, Donald J

    2013-04-25

    We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom. PMID:23531015

  10. A Non-local Reality: Is There a Phase Uncertainty in Quantum Mechanics?

    NASA Astrophysics Data System (ADS)

    Gould, Elizabeth S.; Afshordi, Niayesh

    2015-12-01

    A century after the advent of quantum mechanics and general relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable, conflicts. Motivations for violations of the notion of relativistic locality include the Bell's inequalities for hidden variable theories, the cosmological horizon problem, and Lorentz-violating approaches to quantum geometrodynamics, such as Horava-Lifshitz gravity. Here, we explore a recent proposal for a "real ensemble" non-local description of quantum mechanics, in which "particles" can copy each others' observable values AND phases, independent of their spatial separation. We first specify the exact theory, ensuring that it is consistent and has (ordinary) quantum mechanics as a fixed point, where all particles with the same values for a given observable have the same phases. We then study the stability of this fixed point numerically, and analytically, for simple models. We provide evidence that most systems (in our study) are locally stable to small deviations from quantum mechanics, and furthermore, the phase variance per value of the observable, as well as systematic deviations from quantum mechanics, decay as ˜ (energy × time)^{-2n}, where n ≥ 1. Interestingly, this convergence is controlled by the absolute value of energy (and not energy difference), suggesting a possible connection to gravitational physics. Finally, we discuss different issues related to this theory, as well as potential novel applications for the spectrum of primordial cosmological perturbations and the cosmological constant problem.

  11. What Is a Quantum-Mechanical ``Weak Value'' the Value of?

    NASA Astrophysics Data System (ADS)

    Svensson, Bengt E. Y.

    2013-10-01

    A so called “weak value” of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM paradoxes ( e.g., the so called Three-Box Paradox and Hardy’s Paradox). This requires the weak value to be interpreted as a bona fide property of the system considered, a par with entities like operator mean values and eigenvalues. I question such an interpretation; it has no support in the basic axioms of quantum mechanics and it leads to unreasonable results in concrete situations.

  12. GAMESS as a free quantum-mechanical platform for drug research.

    PubMed

    Alexeev, Yuri; Mazanetz, Michael P; Ichihara, Osamu; Fedorov, Dmitri G

    2012-01-01

    Driven by a steady improvement of computational hardware and significant progress in ab initio method development, quantum-mechanical approaches can now be applied to large biochemical systems and drug design. We review the methods implemented in GAMESS, which are suitable to calculate large biochemical systems. An emphasis is put on the fragment molecular orbital method (FMO) and quantum mechanics interfaced with molecular mechanics (QM/MM). The use of FMO in the protein-ligand binding, structure-activity relationship (SAR) studies, fragment- and structure-based drug design (FBDD/SBDD) is discussed in detail. PMID:23110536

  13. Super classical quantum mechanics: The best interpretation of nonrelativistic quantum mechanics

    NASA Astrophysics Data System (ADS)

    Lamb, Willis E.

    2001-04-01

    It has been shown that Newtonian classical mechanics (NCM) suffers from several kinds of chaotic indeterminacies. That means, a large set of problems treated with NCM gives results which are in wild disagreement with observation. In the present paper, these shortcomings are repaired in a simple, obvious, and essentially unique manner. The NCM theory is thereby transformed into a new theory which is fully equivalent to the Heisenberg, Schrödinger, and Dirac nonrelativistic quantum mechanics, with the vital addition of Born's probabilistic interpretation of the wave function built in from the start. I call this new theory "super classical quantum mechanics" (SCQM). Using Ehrenfest's theorem of 1927, the classical limit of the new theory, SCQM, is seen to give exactly the results expected of the repaired Newtonian theory of classical mechanics.

  14. From quantum mechanics to universal structures of conceptualization and feedback on quantum mechanics

    NASA Astrophysics Data System (ADS)

    Mugur-Schächter, Mioara

    1993-01-01

    In previous works we have established that the spacetime probabilistic organization of the quantum theory is determined by the spacetime characteristics of the operations by which the observer produces the objects to be studied (“states” of microsystems) and obtains qualifications of these. Guided by this first conclusion, we have then built a “general syntax of relativized conceptualization” where any description is explicitly and systematically referred to the two basic epistemic operations by which the conceptor introduces the object to be qualified and then obtains qualifications of it. Inside this syntax there emerges a general typology of the relativized descriptions. Here we show that with respect to this typology the type of the predictive quantum mechanical descriptions acquires a precise definition. It appears that the quantum mechanical formalism has captured and has expressed directly in a mathematical language the most complex form in which can occur a first descriptional phase that lies universally at the bottom of any chain of conceptualization. The main features of the Hilbert-Dirac algorithms are decoded in terms of the general syntax of relativized conceptualization. This renders explicit the semantical contents of the quantum mechanical representations relating each one of these to its mathematical quantum mechanical expression. Basic insufficiencies are thus identified and, correlatively, false problems as well as answers to these, or guides toward answers. Globally the results obtained provide a basis for future attempts at a general mathematical representation of the processes of conceptualization. “Il pourrait, en effet, être dangereux pour l'avenir de la Physique qu'elle se contente trop facilement de purs formalismes, d'images floues et d'explications toutes verbales s'exprimant par des mots à signification imprécise”—Louis de Broglie, Certitudes et Incertitudes de la Science (Albin Michel, Paris, 1965).

  15. Wigner functions for noncommutative quantum mechanics: A group representation based construction

    SciTech Connect

    Chowdhury, S. Hasibul Hassan; Ali, S. Twareque

    2015-12-15

    This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group G{sub NC}, which is the three fold central extension of the Abelian group of ℝ{sup 4}. These representations have been exhaustively studied in earlier papers. The group G{sub NC} is identified with the kinematical symmetry group of noncommutative quantum mechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and those of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only.

  16. The wavefunction of a gravitating shell

    SciTech Connect

    Dokuchaev, V. I. Chernov, S. V.

    2010-10-15

    We have calculated a discrete spectrum and found an exact analytical solution in the form of Meixner polynomials for the wavefunction of a thin gravitating shell in the Reissner-Nordstroem geometry. We show that there is no extreme state in the quantum spectrum of the gravitating shell, as in the case of an extreme black hole.

  17. BOOK REVIEW: Mind, Matter and Quantum Mechanics (2nd edition)

    NASA Astrophysics Data System (ADS)

    Mahler, G.

    2004-07-01

    Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried to expel the non-classical nature of quantum mechanics. More recent proposals intend to complete quantum mechanics not within mechanics proper but on a `higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). I think it is fair to say that in each case the combination is with a subject that, per se, suffers from a very limited understanding that is even more severe than that of quantum mechanics. This was acceptable, though, if it could convincingly be argued that scientific progress desperately needs to join forces. Quantum mechanics of a closed system was a beautiful and well understood theory with its respective state being presented as a point on a deterministic trajectory in Liouville space---not unlike the motion of a classical N-particle system in its 6N-dimensional phase-space. Unfortunately, we need an inside and an outside view, we need an external reference frame, we need an observer. This unavoidable partition is the origin of most of the troubles we have with quantum mechanics. A pragmatic solution is introduced in the form of so-called measurement postulates: one of the various incompatible properties of the system under consideration is supposed to be realized (i.e. to become a fact, to be defined without fundamental dispersion) based on `instantaneous' projections within some externally selected measurement basis. As a result, the theory becomes essentially statistical rather than deterministic

  18. Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems

    ERIC Educational Resources Information Center

    Ozcan, Ozgur; Didis, Nilufer; Tasar, Mehmet Fatih

    2009-01-01

    In this study, students' conceptual difficulties about some basic concepts in quantum mechanics like one-dimensional potential well problems and probability density of tunneling particles were identified. For this aim, a multiple choice instrument named Quantum Mechanics Conceptual Test has been developed by one of the researchers of this study…

  19. Categorization of Quantum Mechanics Problems by Professors and Students

    ERIC Educational Resources Information Center

    Lin, Shih-Yin; Singh, Chandralekha

    2010-01-01

    We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…

  20. Quantum Mechanics from Periodic Dynamics: the bosonic case

    SciTech Connect

    Dolce, Donatello

    2010-05-04

    Enforcing the periodicity hypothesis of the 'old' formulation of Quantum Mechanics we show the possibility for a new scenario where Special Relativity and Quantum Mechanics are unified in a deterministic field theory. A novel interpretation of the AdS/CFT conjecture is discussed.

  1. Developing and Evaluating Animations for Teaching Quantum Mechanics Concepts

    ERIC Educational Resources Information Center

    Kohnle, Antje; Douglass, Margaret; Edwards, Tom J.; Gillies, Alastair D.; Hooley, Christopher A.; Sinclair, Bruce D.

    2010-01-01

    In this paper, we describe animations and animated visualizations for introductory and intermediate-level quantum mechanics instruction developed at the University of St Andrews. The animations aim to help students build mental representations of quantum mechanics concepts. They focus on known areas of student difficulty and misconceptions by…

  2. A comparative review of four formulations of noncommutative quantum mechanics

    NASA Astrophysics Data System (ADS)

    Gouba, Laure

    2016-07-01

    Four formulations of quantum mechanics on noncommutative Moyal phase spaces are reviewed. These are the canonical, path-integral, Weyl-Wigner and systematic formulations. Although all these formulations represent quantum mechanics on a phase space with the same deformed Heisenberg algebra, there are mathematical and conceptual differences which we discuss.

  3. Quantum mechanical features of optically pumped CW FIR lasers

    NASA Technical Reports Server (NTRS)

    Seligson, D.; Leite, J. R. R.; Sanchez, A.; Feld, M. S.; Ducloy, M.

    1977-01-01

    Quantum mechanical predictions for the gain of an optically pumped CW FIR laser are presented for cases in which one or both of the pump and FIR transitions are pressure or Doppler broadened. The results are compared to those based on the rate equation model. Some of the quantum mechanical predictions are verified in CH3OH.

  4. Design and Validation of the Quantum Mechanics Conceptual Survey

    ERIC Educational Resources Information Center

    McKagan, S. B.; Perkins, K. K.; Wieman, C. E.

    2010-01-01

    The Quantum Mechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantum mechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper, we describe the design and validation of the survey, a process that included…

  5. In Defense of a Heuristic Interpretation of Quantum Mechanics

    ERIC Educational Resources Information Center

    Healy, Eamonn F.

    2010-01-01

    Although the presentation of quantum mechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantum mechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift…

  6. Material Phase Causality or a Dynamics-Statistical Interpretation of Quantum Mechanics

    SciTech Connect

    Koprinkov, I. G.

    2010-11-25

    The internal phase dynamics of a quantum system interacting with an electromagnetic field is revealed in details. Theoretical and experimental evidences of a causal relation of the phase of the wave function to the dynamics of the quantum system are presented sistematically for the first time. A dynamics-statistical interpretation of the quantum mechanics is introduced.

  7. Sampling Molecular Conformers in Solution with Quantum Mechanical Accuracy at a Nearly Molecular-Mechanics Cost.

    PubMed

    Rosa, Marta; Micciarelli, Marco; Laio, Alessandro; Baroni, Stefano

    2016-09-13

    We introduce a method to evaluate the relative populations of different conformers of molecular species in solution, aiming at quantum mechanical accuracy, while keeping the computational cost at a nearly molecular-mechanics level. This goal is achieved by combining long classical molecular-dynamics simulations to sample the free-energy landscape of the system, advanced clustering techniques to identify the most relevant conformers, and thermodynamic perturbation theory to correct the resulting populations, using quantum-mechanical energies from density functional theory. A quantitative criterion for assessing the accuracy thus achieved is proposed. The resulting methodology is demonstrated in the specific case of cyanin (cyanidin-3-glucoside) in water solution.

  8. Sampling Molecular Conformers in Solution with Quantum Mechanical Accuracy at a Nearly Molecular-Mechanics Cost.

    PubMed

    Rosa, Marta; Micciarelli, Marco; Laio, Alessandro; Baroni, Stefano

    2016-09-13

    We introduce a method to evaluate the relative populations of different conformers of molecular species in solution, aiming at quantum mechanical accuracy, while keeping the computational cost at a nearly molecular-mechanics level. This goal is achieved by combining long classical molecular-dynamics simulations to sample the free-energy landscape of the system, advanced clustering techniques to identify the most relevant conformers, and thermodynamic perturbation theory to correct the resulting populations, using quantum-mechanical energies from density functional theory. A quantitative criterion for assessing the accuracy thus achieved is proposed. The resulting methodology is demonstrated in the specific case of cyanin (cyanidin-3-glucoside) in water solution. PMID:27494227

  9. Influence of single particle orbital sets and configuration selection on multideterminant wavefunctions in quantum Monte Carlo.

    PubMed

    Clay, Raymond C; Morales, Miguel A

    2015-06-21

    Multideterminant wavefunctions, while having a long history in quantum chemistry, are increasingly being used in highly accurate quantum Monte Carlo calculations. Since the accuracy of QMC is ultimately limited by the quality of the trial wavefunction, multi-Slater determinants wavefunctions offer an attractive alternative to Slater-Jastrow and more sophisticated wavefunction ansatz for several reasons. They can be efficiently calculated, straightforwardly optimized, and systematically improved by increasing the number of included determinants. In spite of their potential, however, the convergence properties of multi-Slater determinant wavefunctions with respect to orbital set choice and excited determinant selection are poorly understood, which hinders the application of these wavefunctions to large systems and solids. In this paper, by performing QMC calculations on the equilibrium and stretched carbon dimer, we find that convergence of the recovered correlation energy with respect to number of determinants can depend quite strongly on basis set and determinant selection methods, especially where there is strong correlation. We demonstrate that properly chosen orbital sets and determinant selection techniques from quantum chemistry methods can dramatically reduce the required number of determinants (and thus the computational cost) to reach a given accuracy, which we argue shows clear need for an automatic QMC-only method for selecting determinants and generating optimal orbital sets. PMID:26093546

  10. Influence of single particle orbital sets and configuration selection on multideterminant wavefunctions in quantum Monte Carlo

    SciTech Connect

    Clay, Raymond C.; Morales, Miguel A.

    2015-06-21

    Multideterminant wavefunctions, while having a long history in quantum chemistry, are increasingly being used in highly accurate quantum Monte Carlo calculations. Since the accuracy of QMC is ultimately limited by the quality of the trial wavefunction, multi-Slater determinants wavefunctions offer an attractive alternative to Slater-Jastrow and more sophisticated wavefunction ansatz for several reasons. They can be efficiently calculated, straightforwardly optimized, and systematically improved by increasing the number of included determinants. In spite of their potential, however, the convergence properties of multi-Slater determinant wavefunctions with respect to orbital set choice and excited determinant selection are poorly understood, which hinders the application of these wavefunctions to large systems and solids. In this paper, by performing QMC calculations on the equilibrium and stretched carbon dimer, we find that convergence of the recovered correlation energy with respect to number of determinants can depend quite strongly on basis set and determinant selection methods, especially where there is strong correlation. We demonstrate that properly chosen orbital sets and determinant selection techniques from quantum chemistry methods can dramatically reduce the required number of determinants (and thus the computational cost) to reach a given accuracy, which we argue shows clear need for an automatic QMC-only method for selecting determinants and generating optimal orbital sets.

  11. Influence of single particle orbital sets and configuration selection on multideterminant wavefunctions in quantum Monte Carlo

    NASA Astrophysics Data System (ADS)

    Clay, Raymond C.; Morales, Miguel A.

    2015-06-01

    Multideterminant wavefunctions, while having a long history in quantum chemistry, are increasingly being used in highly accurate quantum Monte Carlo calculations. Since the accuracy of QMC is ultimately limited by the quality of the trial wavefunction, multi-Slater determinants wavefunctions offer an attractive alternative to Slater-Jastrow and more sophisticated wavefunction ansatz for several reasons. They can be efficiently calculated, straightforwardly optimized, and systematically improved by increasing the number of included determinants. In spite of their potential, however, the convergence properties of multi-Slater determinant wavefunctions with respect to orbital set choice and excited determinant selection are poorly understood, which hinders the application of these wavefunctions to large systems and solids. In this paper, by performing QMC calculations on the equilibrium and stretched carbon dimer, we find that convergence of the recovered correlation energy with respect to number of determinants can depend quite strongly on basis set and determinant selection methods, especially where there is strong correlation. We demonstrate that properly chosen orbital sets and determinant selection techniques from quantum chemistry methods can dramatically reduce the required number of determinants (and thus the computational cost) to reach a given accuracy, which we argue shows clear need for an automatic QMC-only method for selecting determinants and generating optimal orbital sets.

  12. Three Attempts at Two Axioms for Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Rohrlich, Daniel

    The axioms of nonrelativistic quantum mechanics lack clear physical meaning. In particular, they say nothing about nonlocality. Yet quantum mechanics is not only nonlocal, it is twice nonlocal: there are nonlocal quantum correlations, and there is the Aharonov-Bohm effect, which implies that an electric or magnetic field here may act on an electron there. Can we invert the logical hierarchy? That is, can we adopt nonlocality as an axiom for quantum mechanics and derive quantum mechanics from this axiom and an additional axiom of causality? Three versions of these two axioms lead to three different theories, characterized by "maximal nonlocal correlations", "jamming" and "modular energy". Where is quantum mechanics in these theories?

  13. Wavefunction Collapse via a Nonlocal Relativistic Variational Principle

    SciTech Connect

    Harrison, Alan K.

    2012-06-18

    Since the origin of quantum theory in the 1920's, some of its practitioners (and founders) have been troubled by some of its features, including indeterminacy, nonlocality and entanglement. The 'collapse' process described in the Copenhagen Interpretation is suspect for several reasons, and the act of 'measurement,' which is supposed to delimit its regime of validity, has never been unambiguously defined. In recent decades, nonlocality and entanglement have been studied energetically, both theoretically and experimentally, and the theory has been reinterpreted in imaginative ways, but many mysteries remain. We propose that it is necessary to replace the theory by one that is explicitly nonlinear and nonlocal, and does not distinguish between measurement and non-measurement regimes. We have constructed such a theory, for which the phase of the wavefunction plays the role of a hidden variable via the process of zitterbewegung. To capture this effect, the theory must be relativistic, even when describing nonrelativistic phenomena. It is formulated as a variational principle, in which Nature attempts to minimize the sum of two spacetime integrals. The first integral tends to drive the solution toward a solution of the standard quantum mechanical wave equation, and also enforces the Born rule of outcome probabilities. The second integral drives the collapse process. We demonstrate that the new theory correctly predicts the possible outcomes of the electron two-slit experiment, including the infamous 'delayed-choice' variant. We observe that it appears to resolve some long-standing mysteries, but introduces new ones, including possible retrocausality (a cause later than its effect). It is not clear whether the new theory is deterministic.

  14. Perspective: Polarizable continuum models for quantum-mechanical descriptions

    NASA Astrophysics Data System (ADS)

    Lipparini, Filippo; Mennucci, Benedetta

    2016-04-01

    Polarizable continuum solvation models are nowadays the most popular approach to describe solvent effects in the context of quantum mechanical calculations. Unexpectedly, despite their widespread use in all branches of quantum chemistry and beyond, important aspects of both their theoretical formulation and numerical implementation are still not completely understood. In particular, in this perspective we focus on the numerical issues of their implementation when applied to large systems and on the theoretical framework needed to treat time dependent problems and excited states or to deal with electronic correlation. Possible extensions beyond a purely electrostatic model and generalizations to environments beyond common solvents are also critically presented and discussed. Finally, some possible new theoretical approaches and numerical strategies are suggested to overcome the obstacles which still prevent a full exploitation of these models.

  15. Deformation of supersymmetric and conformal quantum mechanics through affine transformations

    NASA Astrophysics Data System (ADS)

    Spiridonov, Vyacheslav

    Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.

  16. Thermal and Quantum Mechanical Noise of a Superfluid Gyroscope

    NASA Technical Reports Server (NTRS)

    Chui, Talso; Penanen, Konstantin

    2004-01-01

    A potential application of a superfluid gyroscope is for real-time measurements of the small variations in the rotational speed of the Earth, the Moon, and Mars. Such rotational jitter, if not measured and corrected for, will be a limiting factor on the resolution potential of a GPS system. This limitation will prevent many automation concepts in navigation, construction, and biomedical examination from being realized. We present the calculation of thermal and quantum-mechanical phase noise across the Josephson junction of a superfluid gyroscope. This allows us to derive the fundamental limits on the performance of a superfluid gyroscope. We show that the fundamental limit on real-time GPS due to rotational jitter can be reduced to well below 1 millimeter/day. Other limitations and their potential mitigation will also be discussed.

  17. QUANTUM MECHANICS. Quantum squeezing of motion in a mechanical resonator.

    PubMed

    Wollman, E E; Lei, C U; Weinstein, A J; Suh, J; Kronwald, A; Marquardt, F; Clerk, A A; Schwab, K C

    2015-08-28

    According to quantum mechanics, a harmonic oscillator can never be completely at rest. Even in the ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. Using microwave frequency radiation pressure, we have manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state. We also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. Our results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion.

  18. Evanescent radiation, quantum mechanics and the Casimir effect

    NASA Technical Reports Server (NTRS)

    Schatten, Kenneth H.

    1989-01-01

    An attempt to bridge the gap between classical and quantum mechanics and to explain the Casimir effect is presented. The general nature of chaotic motion is discussed from two points of view: the first uses catastrophe theory and strange attractors to describe the deterministic view of this motion; the underlying framework for chaos in these classical dynamic systems is their extreme sensitivity to initial conditions. The second interpretation refers to randomness associated with probabilistic dynamics, as for Brownian motion. The present approach to understanding evanescent radiation and its relation to the Casimir effect corresponds to the first interpretation, whereas stochastic electrodynamics corresponds to the second viewpoint. The nonlinear behavior of the electromagnetic field is also studied. This well-understood behavior is utilized to examine the motions of two orbiting charges and shows a closeness between the classical behavior and the quantum uncertainty principle. The evanescent radiation is used to help explain the Casimir effect.

  19. Conservation of information and the foundations of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Chiribella, Giulio; Scandolo, Carlo Maria

    2015-05-01

    We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory [1, 2]. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features. We first illustrate two very primitive features, expressed by the axioms of causality and purity-preservation, which are satisfied by both classical and quantum theory. We then discuss the axiom of purification, which expresses a strong version of the Conservation of Information and captures the core of a vast number of protocols in quantum information. Purification is a highly non-classical feature and leads directly to the emergence of entanglement at the purely conceptual level, without any reference to the superposition principle. Supplemented by a few additional requirements, satisfied by classical and quantum theory, it provides a complete axiomatic characterization of quantum theory for finite dimensional systems.

  20. Supersymmetric quantum mechanics and Painlevé equations

    SciTech Connect

    Bermudez, David; Fernández C, David J.

    2014-01-08

    In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order the potential is determined by solutions to Painlevé IV (PIV) and Painlevé V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.

  1. Deformation of supersymmetric and conformal quantum mechanics through affine transformations

    NASA Technical Reports Server (NTRS)

    Spiridonov, Vyacheslav

    1993-01-01

    Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.

  2. Quantum mechanics of Drude oscillators with full Coulomb interaction

    NASA Astrophysics Data System (ADS)

    Sadhukhan, M.; Manby, Frederick R.

    2016-09-01

    Drude oscillators provide a harmonic description of charge fluctuations and are widely studied as a model system and for ab initio calculations. In the dipole approximation the Hamiltonian describing the interaction of Drudes is quadratic, so it can be diagonalized exactly, but the energy diverges at short range. Here we consider the quantum mechanics of Drude oscillators interacting through the full Coulombic Hamiltonian for which the interaction energy does not have this defect. This protypical model for interactions between matter includes electrostatics, induction, and dispersion. Potential energy curves for rare-gas dimers are very closely matched by Drude correlation energies plus a single exponential function. The exact and accurate results presented here help to delineate between the basic properties of the physical model and the effects that arise from the dipole approximation.

  3. The equivalence principle of quantum mechanics: Uniqueness theorem

    SciTech Connect

    Faraggi, A.E.; Matone, M.

    1997-10-28

    Recently the authors showed that the postulated diffeomorphic equivalence of states implies quantum mechanics. This approach takes the canonical variables to be dependent by the relation p = {partial_derivative}{sub q}S{sub 0} and exploits a basic GL(2,C)-symmetry which underlies the canonical formalism. In particular, they looked for the special transformations leading to the free system with vanishing energy. Furthermore, they saw that while on the one hand the equivalence principle cannot be consistently implemented in classical mechanics, on the other it naturally led to the quantum analogue of the Hamilton-Jacobi equation, thus implying the Schroedinger equation. In this letter they show that actually the principle uniquely leads to this solution. The authors also express the canonical and Schroedinger equations by means of the brackets recently introduced in the framework of N = 2 SYM. These brackets are the analogue of the Poisson brackets with the canonical variables taken as dependent.

  4. Quantum mechanical studies of DNA and LNA.

    PubMed

    Koch, Troels; Shim, Irene; Lindow, Morten; Ørum, Henrik; Bohr, Henrik G

    2014-04-01

    Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies of the electrostatic potentials were compared among model oligonucleotides, and it was observed that small structural modifications induce global changes in the molecular structure and surface potentials. Since ligand structure and electrostatic potential complementarity with a receptor is a determinant for the bonding pattern between molecules, minor chemical modifications may have profound changes in the interaction profiles of oligonucleotides, possibly leading to changes in pharmacological properties. The QM modeling data can be used to understand earlier observations of antisense oligonucleotide properties, that is, the observation that small structural changes in oligonucleotide composition may lead to dramatic shifts in phenotypes. These observations should be taken into account in future oligonucleotide drug discovery, and by focusing more on non RNA target interactions it should be possible to utilize the exhibited property diversity of oligonucleotides to produce improved antisense drugs.

  5. Quantum mechanical light harvesting mechanisms in photosynthesis

    NASA Astrophysics Data System (ADS)

    Scholes, Gregory

    2012-02-01

    More than 10 million billion photons of light strike a leaf each second. Incredibly, almost every red-coloured photon is captured by chlorophyll pigments and initiates steps to plant growth. Last year we reported that marine algae use quantum mechanics in order to optimize photosynthesis [1], a process essential to its survival. These and other insights from the natural world promise to revolutionize our ability to harness the power of the sun. In a recent review [2] we described the principles learned from studies of various natural antenna complexes and suggested how to utilize that knowledge to shape future technologies. We forecast the need to develop ways to direct and regulate excitation energy flow using molecular organizations that facilitate feedback and control--not easy given that the energy is only stored for a billionth of a second. In this presentation I will describe new results that explain the observation and meaning of quantum-coherent energy transfer. [4pt] [1] Elisabetta Collini, Cathy Y. Wong, Krystyna E. Wilk, Paul M. G. Curmi, Paul Brumer, and Gregory D. Scholes, ``Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature'' Nature 463, 644-648 (2010).[0pt] [2] Gregory D. Scholes, Graham R. Fleming, Alexandra Olaya-Castro and Rienk van Grondelle, ``Lessons from nature about solar light harvesting'' Nature Chem. 3, 763-774 (2011).

  6. Quantum Mechanical Studies of DNA and LNA

    PubMed Central

    Shim, Irene; Lindow, Morten; Ørum, Henrik

    2014-01-01

    Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies of the electrostatic potentials were compared among model oligonucleotides, and it was observed that small structural modifications induce global changes in the molecular structure and surface potentials. Since ligand structure and electrostatic potential complementarity with a receptor is a determinant for the bonding pattern between molecules, minor chemical modifications may have profound changes in the interaction profiles of oligonucleotides, possibly leading to changes in pharmacological properties. The QM modeling data can be used to understand earlier observations of antisense oligonucleotide properties, that is, the observation that small structural changes in oligonucleotide composition may lead to dramatic shifts in phenotypes. These observations should be taken into account in future oligonucleotide drug discovery, and by focusing more on non RNA target interactions it should be possible to utilize the exhibited property diversity of oligonucleotides to produce improved antisense drugs. PMID:24491259

  7. Extending quantum mechanics entails extending special relativity

    NASA Astrophysics Data System (ADS)

    Aravinda, S.; Srikanth, R.

    2016-05-01

    The complementarity between signaling and randomness in any communicated resource that can simulate singlet statistics is generalized by relaxing the assumption of free will in the choice of measurement settings. We show how to construct an ontological extension for quantum mechanics (QMs) through the oblivious embedding of a sound simulation protocol in a Newtonian spacetime. Minkowski or other intermediate spacetimes are ruled out as the locus of the embedding by virtue of hidden influence inequalities. The complementarity transferred from a simulation to the extension unifies a number of results about quantum non-locality, and implies that special relativity has a different significance for the ontological model and for the operational theory it reproduces. Only the latter, being experimentally accessible, is required to be Lorentz covariant. There may be certain Lorentz non-covariant elements at the ontological level, but they will be inaccessible at the operational level in a valid extension. Certain arguments against the extendability of QM, due to Conway and Kochen (2009) and Colbeck and Renner (2012), are attributed to their assumption that the spacetime at the ontological level has Minkowski causal structure.

  8. Double-slit experiment with single wave-driven particles and its relation to quantum mechanics

    NASA Astrophysics Data System (ADS)

    Andersen, Anders; Madsen, Jacob; Reichelt, Christian; Rosenlund Ahl, Sonja; Lautrup, Benny; Ellegaard, Clive; Levinsen, Mogens T.; Bohr, Tomas

    2015-07-01

    In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006), 10.1103/PhysRevLett.97.154101] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantum mechanics.

  9. Double-slit experiment with single wave-driven particles and its relation to quantum mechanics.

    PubMed

    Andersen, Anders; Madsen, Jacob; Reichelt, Christian; Rosenlund Ahl, Sonja; Lautrup, Benny; Ellegaard, Clive; Levinsen, Mogens T; Bohr, Tomas

    2015-07-01

    In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantum mechanics.

  10. Enriching Elementary Quantum Mechanics with the Computer: Self-Consistent Field Problems in One Dimension

    ERIC Educational Resources Information Center

    Bolemon, Jay S.; Etzold, David J.

    1974-01-01

    Discusses the use of a small computer to solve self-consistent field problems of one-dimensional systems of two or more interacting particles in an elementary quantum mechanics course. Indicates that the calculation can serve as a useful introduction to the iterative technique. (CC)

  11. Weinberg's nonlinear quantum mechanics and the Einstein-Podolsky-Rosen paradox

    NASA Technical Reports Server (NTRS)

    Polchinski, Joseph

    1991-01-01

    The constraints imposed on observables by the requirement that transmission not occur in the Einstein-Podolsky-Rosen (EPR) experiment are determined, leading to a different treatment of separated systems from that originally proposed by Weinberg (1989). It is found that forbidding EPR communication in nonlinear quantum mechanics necessarily leads to another sort of unusual communication: that between different branches of the wave function.

  12. A fast quantum mechanics based contour extraction algorithm

    NASA Astrophysics Data System (ADS)

    Lan, Tian; Sun, Yangguang; Ding, Mingyue

    2009-02-01

    A fast algorithm was proposed to decrease the computational cost of the contour extraction approach based on quantum mechanics. The contour extraction approach based on quantum mechanics is a novel method proposed recently by us, which will be presented on the same conference by another paper of us titled "a statistical approach to contour extraction based on quantum mechanics". In our approach, contour extraction was modeled as the locus of a moving particle described by quantum mechanics, which is obtained by the most probable locus of the particle simulated in a large number of iterations. In quantum mechanics, the probability that a particle appears at a point is equivalent to the square amplitude of the wave function. Furthermore, the expression of the wave function can be derived from digital images, making the probability of the locus of a particle available. We employed the Markov Chain Monte Carlo (MCMC) method to estimate the square amplitude of the wave function. Finally, our fast quantum mechanics based contour extraction algorithm (referred as our fast algorithm hereafter) was evaluated by a number of different images including synthetic and medical images. It was demonstrated that our fast algorithm can achieve significant improvements in accuracy and robustness compared with the well-known state-of-the-art contour extraction techniques and dramatic reduction of time complexity compared to the statistical approach to contour extraction based on quantum mechanics.

  13. Review of student difficulties in upper-level quantum mechanics

    NASA Astrophysics Data System (ADS)

    Singh, Chandralekha; Marshman, Emily

    2015-12-01

    [This paper is part of the Focused Collection on Upper Division Physics Courses.] Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical mechanics and quantum mechanics are very different. Here, we review research on student reasoning difficulties in learning upper-level quantum mechanics and research on students' problem-solving and metacognitive skills in these courses. Some of these studies were multiuniversity investigations. The investigations suggest that there is large diversity in student performance in upper-level quantum mechanics regardless of the university, textbook, or instructor, and many students in these courses have not acquired a functional understanding of the fundamental concepts. The nature of reasoning difficulties in learning quantum mechanics is analogous to reasoning difficulties found via research in introductory physics courses. The reasoning difficulties were often due to overgeneralizations of concepts learned in one context to another context where they are not directly applicable. Reasoning difficulties in distinguishing between closely related concepts and in making sense of the formalism of quantum mechanics were common. We conclude with a brief summary of the research-based approaches that take advantage of research on student difficulties in order to improve teaching and learning of quantum mechanics.

  14. Nonstationary Quantum Mechanics. III. Quantum Mechanics Does Not Incorporate Classical Physics

    NASA Astrophysics Data System (ADS)

    Todorov, Nickola Stefanov

    1981-01-01

    It is shown that disagreement between the prediction of classical and conventional quantum mechanics about momentum probabilities exists in the case of a quasiclassical motion. The discussion is based on the detailed consideration of two specific potentials: U( x)= x and the oscillatory potential U( x)= mω 2 x 2/2. The results of the present Part III represent a further development of the idea in Todorov (1980) about the possible inefficiency of conventional theory in the case of potentials swiftly varying with time.

  15. Development and validation of an achievement test in introductory quantum mechanics: The Quantum Mechanics Visualization Instrument (QMVI)

    NASA Astrophysics Data System (ADS)

    Cataloglu, Erdat

    The purpose of this study was to construct a valid and reliable multiple-choice achievement test to assess students' understanding of core concepts of introductory quantum mechanics. Development of the Quantum Mechanics Visualization Instrument (QMVI) occurred across four successive semesters in 1999--2001. During this time 213 undergraduate and graduate students attending the Pennsylvania State University (PSU) at University Park and Arizona State University (ASU) participated in this development and validation study. Participating students were enrolled in four distinct groups of courses: Modern Physics, Undergraduate Quantum Mechanics, Graduate Quantum Mechanics, and Chemistry Quantum Mechanics. Expert panels of professors of physics experienced in teaching quantum mechanics courses and graduate students in physics and science education established the core content and assisted in the validating of successive versions of the 24-question QMVI. Instrument development was guided by procedures outlined in the Standards for Educational and Psychological Testing (AERA-APA-NCME, 1999). Data gathered in this study provided information used in the development of successive versions of the QMVI. Data gathered in the final phase of administration of the QMVI also provided evidence that the intended score interpretation of the QMVI achievement test is valid and reliable. A moderate positive correlation coefficient of 0.49 was observed between the students' QMVI scores and their confidence levels. Analyses of variance indicated that students' scores in Graduate Quantum Mechanics and Undergraduate Quantum Mechanics courses were significantly higher than the mean scores of students in Modern Physics and Chemistry Quantum Mechanics courses (p < 0.05). That finding is consistent with the additional understanding and experience that should be anticipated in graduate students and junior-senior level students over sophomore physics majors and majors in another field. The moderate

  16. Model Wavefunctions For Non-Abelian Quasiparticles

    NASA Astrophysics Data System (ADS)

    Bernevig, B. Andrei; Haldane, F. D. M.

    2008-03-01

    We present model wavefunctions for quasiparticle (as opposed to quasihole)excitations of the Zk parafermion sequence (Laughlin/Moore-Read/Read-Rezayi) of Fractional Quantum Hall states. These states satisfy two generalized clustering conditions: they vanish when either a cluster of k+2 electrons is put together, or when two clusters of k+1 electrons are formed at different positions. For Abelian Fractional Quantum Hall states (k=1), our construction reproduces the Jain quasielectron wavefunction, and elucidates the difference between the Jain and Laughlin quasiparticle constructions. For two (or more) quasiparticles, our states differ from those constructed using Jain's method. By adding our quasiparticles to the Laughlin state, we obtain a hierarchy scheme which gives rise to a non-abelian ν=2 5 FQH state.

  17. Simple example of definitions of truth, validity, consistency, and completeness in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Benioff, Paul

    1999-06-01

    Besides their use for efficient computation, quantum computers and quantum robots form a base for studying quantum systems that create valid physical theories using mathematics and physics. If quantum mechanics is universally applicable, then quantum mechanics must describe its own validation by these quantum systems. An essential part of this process is the development of a coherent theory of mathematics and quantum-mechanics together. It is expected that such a theory will include a coherent combination of mathematical logical concepts with quantum mechanics. That this might be possible is shown here by defining truth, validity, consistency, and completeness for a quantum-mechanical version of a simple (classical) expression enumeration machine described by Smullyan. Some of the expressions are chosen as sentences denoting the presence or absence of other expressions in the enumeration. Two of the sentences are self-referential. It is seen that, for an interpretation based on a Feynman path sum over expression paths, truth, consistency, and completeness for the quantum system have different properties than for the classical system. For instance, the truth of a sentence S is defined only on those paths containing S. It is undefined elsewhere. Also S and its negation can both be true provided they appear on separate paths. This satisfies the definition of consistency. The definitions of validity and completeness connect the dynamics of the system to the truth of the sentences. It is proved that validity implies consistency. It is seen that the requirements of validity and maximal completeness strongly restrict the allowable dynamics for the quantum system. Aspects of the existence of a valid, maximally complete dynamics are discussed. An exponentially efficient quantum computer is described that is also valid and complete for the set of sentences considered here.

  18. Role of the observer in quantum mechanics and the Zeno paradox

    NASA Astrophysics Data System (ADS)

    Singh, Ishwar; Whitaker, M. A. B.

    1982-10-01

    We discuss the role of the observer in quantum mechanics. We briefly discuss various interpretations of quantum-mechanical measurement currently used in the literature. Then we point out the difficulty in deciding what occurrences should be classified as ''observations.'' Using the Copenhagen Interpretation, we discuss the effect of successive measurements on the decay rate of an unstable quantum system. For two types of systems, those with a small finite number of decay levels and those with a continuum or semicontinuum, we review the decay behavior, and in the latter case distinguish between: small time behavior, with survival probability falling off as t2; the intermediate region, where it varies exponentially with time; and the long-time region, where the decay is less than exponential. If we cannot define an observation, we show that only an exact exponential decay is allowed. Attempts at solutions of this difficulty are mentioned. Lastly, we take an example of a polarized beam of light passing through an optically active medium, and discuss the process of successive measurement from classical and quantum mechanical viewpoints. The two descriptions appear to differ because we are implicitly considering two different experimental arrangements. We put forward classical and quantum-mechanical descriptions of each experiment.

  19. The exact molecular wavefunction as a product of an electronic and a nuclear wavefunction

    SciTech Connect

    Cederbaum, Lorenz S.

    2013-06-14

    The Born-Oppenheimer approximation is a basic approximation in molecular science. In this approximation, the total molecular wavefunction is written as a product of an electronic and a nuclear wavefunction. Hunter [Int. J. Quantum Chem. 9, 237 (1975)] has argued that the exact total wavefunction can also be factorized as such a product. In the present work, a variational principle is introduced which shows explicitly that the total wavefunction can be exactly written as such a product. To this end, a different electronic Hamiltonian has to be defined. The Schroedinger equation for the electronic wavefunction follows from the variational ansatz and is presented. As in the Born-Oppenheimer approximation, the nuclear motion is shown to proceed in a potential which is the electronic energy. In contrast to the Born-Oppenheimer approximation, the separation of the center of mass can be carried out exactly. The electronic Hamiltonian and the equation of motion of the nuclei resulting after the exact separation of the center of mass motion are explicitly given. A simple exactly solvable model is used to illustrate some aspects of the theory.

  20. The von Neumann model of measurement in quantum mechanics

    SciTech Connect

    Mello, Pier A.

    2014-01-08

    We describe how to obtain information on a quantum-mechanical system by coupling it to a probe and detecting some property of the latter, using a model introduced by von Neumann, which describes the interaction of the system proper with the probe in a dynamical way. We first discuss single measurements, where the system proper is coupled to one probe with arbitrary coupling strength. The goal is to obtain information on the system detecting the probe position. We find the reduced density operator of the system, and show how Lüders rule emerges as the limiting case of strong coupling. The von Neumann model is then generalized to two probes that interact successively with the system proper. Now we find information on the system by detecting the position-position and momentum-position correlations of the two probes. The so-called 'Wigner's formula' emerges in the strong-coupling limit, while 'Kirkwood's quasi-probability distribution' is found as the weak-coupling limit of the above formalism. We show that successive measurements can be used to develop a state-reconstruction scheme. Finally, we find a generalized transform of the state and the observables based on the notion of successive measurements.

  1. Quantum Mechanics and the Social Sciences: After Hermeneutics.

    ERIC Educational Resources Information Center

    Heelan, Patrick A.

    1995-01-01

    An analysis of the hermeneutical aspect of quantum mechanical measurement reveals close analogs with the hermeneutical social/historical sciences. Suggests that the hermeneutical analysis of science requires the move from the epistemological attitude to an ontological view. (LZ)

  2. A proof of von Neumann's postulate in Quantum Mechanics

    SciTech Connect

    Conte, Elio

    2010-05-04

    A Clifford algebraic analysis is explained. It gives proof of von Neumann's postulate on quantum measurement. It is of basic significance to explain the problem of quantum wave function reduction in quantum mechanics.

  3. Probabilistic Approach to Teaching the Principles of Quantum Mechanics

    ERIC Educational Resources Information Center

    Santos, Emilio

    1976-01-01

    Approaches the representation of quantum mechanics through Hilbert space postulates. Demonstrates that if the representation is to be accurate, an evolution operator of the form of a Hamiltonian must be used. (CP)

  4. Chirality, quantum mechanics, and biological determinism

    NASA Astrophysics Data System (ADS)

    Davies, P. C. W.

    2006-08-01

    life with biochemical make-up resembling that of known life. Whilst the experimental search for a second sample of life - possibly by detecting a chiral "anomaly" - continues, some theoretical investigations may be pursued to narrow down the options. Chiral determinism would be an intrinsically quantum process. There are hints that quantum mechanics plays a key role in biology, but the claim remains contentious. Here I review some of the evidence for quantum aspects of biology. I also summarize some proposals for testing biological determinism by seeking evidence for a multiple genesis events on Earth, and for identifying extant "alien microbes" - micro-organisms descended from an independent origin from familiar life.

  5. Scattering in the Euclidean formulation of relativistic quantum mechanics

    NASA Astrophysics Data System (ADS)

    Polyzou, Wayne

    2013-10-01

    Euclidean relativistic quantum mechanics is a formulation of relativistic quantum mechanics based on the Osterwalder-Schrader reconstruction theorem that exploits the logical independence of locality from the rest of the axioms of Euclidean field theory. I discuss the properties of Euclidean Green functions necessary for the existence of Møller wave operators and the construction of these wave operators in this formalism. Supported by the US Department of Energy, Grant - DE-AC02-81ER40038.

  6. Interpreting Quantum Mechanics according to a Pragmatist Approach

    NASA Astrophysics Data System (ADS)

    Bächtold, Manuel

    2008-09-01

    The aim of this paper is to show that quantum mechanics can be interpreted according to a pragmatist approach. The latter consists, first, in giving a pragmatic definition to each term used in microphysics, second, in making explicit the functions any theory must fulfil so as to ensure the success of the research activity in microphysics, and third, in showing that quantum mechanics is the only theory which fulfils exactly these functions.

  7. QUANTUM MECHANICS: Enhanced: Schrodinger's Cat Is Out of the Hat.

    PubMed

    Tesche, C

    2000-10-27

    In 1935, Erwin Schrödinger suggested his famous gedanken experiment of the cat that is simultaneously "dead" and "alive" inside its box until the box is opened. But as Tesche explains in her Perspective, such a macroscopic manifestation of quantum mechanics has remained elusive until recently. The experiments by van der Wal et al. are an important step toward demonstrating that quantum mechanics can describe macroscopic phenomena. The approach may be exploited in quantum computing and quantum cryptography.

  8. Bohmian mechanics with complex action: a new trajectory-based formulation of quantum mechanics.

    PubMed

    Goldfarb, Yair; Degani, Ilan; Tannor, David J

    2006-12-21

    In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10(-7) calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.

  9. Some Novel Thought Experiments Involving Foundations of Quantum Mechanics and Quantum Information

    NASA Astrophysics Data System (ADS)

    Akhavan, Omid

    2004-02-01

    In this thesis, we have proposed some novel thought experiments involving foundations of quantum mechanics and quantum information theory, using quantum entanglement property. Concerning foundations of quantum mechanics, we have suggested some typical systems including two correlated particles which can distinguish between the two famous theories of quantum mechanics, i.e. the standard and Bohmian quantum mechanics, at the individual level of pair of particles. Meantime, the two theories present the same predictions at the ensemble level of particles. Regarding quantum information theory, two theoretical quantum communication schemes including quantum dense coding and quantum teleportation schemes have been proposed by using entangled spatial states of two EPR particles shared between two parties. It is shown that the rate of classical information gain in our dense coding scheme is greater than some previously proposed multi-qubit protocols by a logarithmic factor dependent on the dimension of Hilbert space. The proposed teleportation scheme can provide a complete wave function teleportation of an object having other degrees of freedom in our three-dimensional space, for the first time. All required unitary operators which are necessary in our state preparation and Bell state measurement processes are designed using symmetric normalized Hadamard matrix, some basic gates and one typical conditional gate, which are introduced here for the first time.

  10. Quantum Mechanics and the Principle of Maximal Variety

    NASA Astrophysics Data System (ADS)

    Smolin, Lee

    2016-06-01

    Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to an ensemble of subsystems of the universe with identical constituents and similar preparations and environments. A new kind of interaction is posited amongst such similar subsystems which acts to increase their distinctiveness, by extremizing the variety. In the limit of large numbers of similar subsystems this interaction is shown to give rise to Bohm's quantum potential. As a result the probability distribution for the ensemble is governed by the Schroedinger equation. The measurement problem is naturally and simply solved. Microscopic systems appear statistical because they are members of large ensembles of similar systems which interact non-locally. Macroscopic systems are unique, and are not members of any ensembles of similar systems. Consequently their collective coordinates may evolve deterministically. This proposal could be tested by constructing quantum devices from entangled states of a modest number of quits which, by its combinatorial complexity, can be expected to have no natural copies.

  11. Nonrelativistic quantum mechanics with consideration of influence of fundamental environment

    SciTech Connect

    Gevorkyan, A. S.

    2013-08-15

    Spontaneous transitions between bound states of an atomic system, the 'Lamb Shift' of energy levels and many other phenomena in real nonrelativistic quantum systems are connected with the influence of the quantum vacuum fluctuations (fundamental environment (FE)), which are impossible to consider in the framework of standard quantum-mechanical approaches. The joint system quantum system (QS) and FE is described in the framework of the stochastic differential equation (SDE) of Langevin-Schroedinger type and is defined on the extended space Double-Struck-Capital-R {sup 3} Circled-Times {Xi}{sup n}, where Double-Struck-Capital-R {sup 3} and {Xi}{sup n} are the Euclidean and functional spaces, respectively. The method of stochastic density matrix is developed and the von Neumann equation for reduced density matrix of QS with FE is generalized. The entropy of QS entangled with FE is defined and investigated. It is proved that the interaction of QS with the environment leads to emerging structures of various topologies which present new quantum-field properties of QS. It is shown that when the physical system (irrelatively to its being micro ormacro) breaks up into two fragments by means of FE, there arises between these fragments a nonpotential interaction which does not disappear at large distances.

  12. Annular tautomerism: experimental observations and quantum mechanics calculations.

    PubMed

    Cruz-Cabeza, Aurora J; Schreyer, Adrian; Pitt, William R

    2010-06-01

    The use of MP2 level quantum mechanical (QM) calculations on isolated heteroaromatic ring systems for the prediction of the tautomeric propensities of whole molecules in a crystalline environment was examined. A Polarisable Continuum Model was used in the calculations to account for environment effects on the tautomeric relative stabilities. The calculated relative energies of tautomers were compared to relative abundances within the Cambridge Structural Database (CSD) and the Protein Data Bank (PDB). The work was focussed on 84 annular tautomeric forms of 34 common ring systems. Good agreement was found between the calculations and the experimental data even if the quantity of these data was limited in many cases. The QM results were compared to those produced by much faster semiempirical calculations. In a search for other sources of the useful experimental data, the relative numbers of known compounds in which prototropic positions were often substituted by heavy atoms were also analysed. A scheme which groups all annular tautomeric transformations into 10 classes was developed. The scheme was designed to encompass a comprehensive set of known and theoretically possible tautomeric ring systems generated as part of a previous study. General trends across analogous ring systems were detected as a result. The calculations and statistics collected on crystallographic data as well as the general trends observed should be useful for the better modelling of annular tautomerism in the applications such as computer-aided drug design, small molecule crystal structure prediction, the naming of compounds and the interpretation of protein-small molecule crystal structures.

  13. Quantum revivals and magnetization tunneling in effective spin systems

    NASA Astrophysics Data System (ADS)

    Krizanac, M.; Altwein, D.; Vedmedenko, E. Y.; Wiesendanger, R.

    2016-03-01

    Quantum mechanical objects or nano-objects have been proposed as bits for information storage. While time-averaged properties of magnetic, quantum-mechanical particles have been extensively studied experimentally and theoretically, experimental investigations of the real time evolution of magnetization in the quantum regime were not possible until recent developments in pump-probe techniques. Here we investigate the quantum dynamics of effective spin systems by means of analytical and numerical treatments. Particular attention is paid to the quantum revival time and its relation to the magnetization tunneling. The quantum revival time has been initially defined as the recurrence time of a total wave-function. Here we show that the quantum revivals of wave-functions and expectation values in spin systems may be quite different which gives rise to a more sophisticated definition of the quantum revival within the realm of experimental research. Particularly, the revival times for integer spins coincide which is not the case for half-integer spins. Furthermore, the quantum revival is found to be shortest for integer ratios between the on-site anisotropy and an external magnetic field paving the way to novel methods of anisotropy measurements. We show that the quantum tunneling of magnetization at avoided level crossing is coherent to the quantum revival time of expectation values, leading to a connection between these two fundamental properties of quantum mechanical spins.

  14. QuVis interactive simulations: tools to support quantum mechanics instruction

    NASA Astrophysics Data System (ADS)

    Kohnle, Antje

    2015-04-01

    Quantum mechanics holds a fascination for many students, but its mathematical complexity and counterintuitive results can present major barriers. The QuVis Quantum Mechanics Visualization Project (www.st-andrews.ac.uk/physics/quvis) aims to overcome these issues through the development and evaluation of interactive simulations with accompanying activities for the learning and teaching of quantum mechanics. Over 90 simulations are now available on the QuVis website. One collection of simulations is embedded in the Institute of Physics Quantum Physics website (quantumphysics.iop.org), which consists of freely available resources for an introductory course in quantum mechanics starting from two-level systems. Simulations support model-building by reducing complexity, focusing on fundamental ideas and making the invisible visible. They promote engaged exploration, sense-making and linking of multiple representations, and include high levels of interactivity and direct feedback. Simulations are research-based and evaluation with students informs all stages of the development process. Simulations are iteratively refined using student feedback in individual observation sessions and in-class trials. Evaluation has shown that the simulations can help students learn quantum mechanics concepts at both the introductory and advanced undergraduate level and that students perceive simulations to be beneficial to their learning. Recent activity includes the launch of a new collection of HTML5 simulations that run on both desktop and tablet-based devices and the introduction of a goal and reward structure in simulations through the inclusion of challenges. This presentation will give an overview of the QuVis resources, highlight recent work and outline future plans. QuVis is supported by the UK Institute of Physics, the UK Higher Education Academy and the University of St Andrews.

  15. Cubic Wavefunction Deformation of Compressed Atoms

    NASA Astrophysics Data System (ADS)

    Portela, Pedro Calvo; Llanes-Estrada, Felipe J.

    2015-05-01

    We hypothesize that in a non-metallic crystalline structure under extreme pressures, atomic wavefunctions deform to adopt a reduced rotational symmetry consistent with minimizing interstitial space in the crystal. We exemplify with a simple numeric variational calculation that yields the energy cost of this deformation for Helium to 25 %. Balancing this with the free energy gained by tighter packing we obtain the pressures required to effect such deformation. The consequent modification of the structure suggests a decrease in the resistance to tangential stress, and an associated decrease of the crystal's shear modulus. The atomic form factor is also modified. We also compare with neutron matter in the interior of compact stars.

  16. Fluctuations of wavefunctions about their classical average

    NASA Astrophysics Data System (ADS)

    Benet, L.; Flores, J.; Hernández-Saldaña, H.; Izrailev, F. M.; Leyvraz, F.; Seligman, T. H.

    2003-02-01

    Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations of the quantum wavefunctions around the classical value are discussed. A simple random matrix model leads to a Gaussian distribution of the amplitudes whose width is determined by the classical shape of the eigenfunction. To compare this prediction with numerical calculations in chaotic models of coupled quartic oscillators, we develop a rescaling method for the components. The expectations are broadly confirmed, but deviations due to scars are observed. This effect is much reduced when both Hamiltonians have chaotic dynamics.

  17. Testing the foundations of quantum mechanics with multi-path interferometers

    NASA Astrophysics Data System (ADS)

    Keil, Robert; Kauten, Thomas; Kaufmann, Thomas; Pressl, Benedikt; Heilmann, Rene; Szameit, Alexander; Weihs, Gregor

    2015-05-01

    Born's rule is one of the fundamental axioms of quantum mechanics and states that the probability density equates the squared magnitude of the wavefunction. Axioms in physics can't be theoretically proven, but only tested against experiments. Born's rule dictates the absence of higher order interference. Therefore, it can be tested by measuring the output signal of a multi-path interferometer with individually blockable paths. In this contribution, we present our latest results in this respect, improving previous experiments by two orders of magnitude in accuracy and precision. To this end, we implemented a five-path Mach-Zehnder interferometer in free space with improved power and phase stabilisation and increased photon flux. After compensating for the systematic effect of detector nonlinearities, we could bound the relative magnitude of higher order interferences to better than 10-4. In order to reduce this bound further, we have started working towards optically integrated interferometers, which promise reduced footprint and superior stability. Our first attempt in this direction is a semi-integrated solution. In this Michelson-configuration, external micromirrors are individually moved to modulate the effective transmission of each interferometer arm. We present our preliminary results obtained from this waveguide interferometer, discuss its current limitations and indicate ways to overcome them.

  18. Attosecond delays in photoionization: time and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Maquet, Alfred; Caillat, Jérémie; Taïeb, Richard

    2014-10-01

    This article addresses topics regarding time measurements performed on quantum systems. The motivation is linked to the advent of ‘attophysics’ which makes feasible to follow the motion of electrons in atoms and molecules, with time resolution at the attosecond (1 as = 10-18 s) level, i.e. at the natural scale for electronic processes in these systems. In this context, attosecond ‘time-delays’ have been recently measured in experiments on photoionization and the question arises if such advances could cast a new light on the still active discussion on the status of the time variable in quantum mechanics. One issue still debatable is how to decide whether one can define a quantum time operator with eigenvalues associated to measurable ‘time-delays’, or time is a parameter, as it is implicit in the Newtonian classical mechanics. One objective of this paper is to investigate if the recent attophysics-based measurements could shed light on this parameter-operator conundrum. To this end, we present here the main features of the theory background, followed by an analysis of the experimental schemes that have been used to evidence attosecond ‘time-delays’ in photoionization. Our conclusion is that these results reinforce the view that time is a parameter which cannot be defined without reference to classical mechanics.

  19. Communication: Imaging wavefunctions in dissociative photoionization

    NASA Astrophysics Data System (ADS)

    Scott Hopkins, W.; Mackenzie, Stuart R.

    2011-08-01

    The dissociative ionization dynamics of excited electronic states of the xenon dimer, Xe2, have been studied using velocity map ion imaging (VMI). A one-colour, (2+1) resonant excitation scheme was employed to first excite and then ionize selected vibrational levels of the Xe2 6p 2[1/2]0 0_g^ + Rydberg state. Cationic fragments were then detected by the VMI. The data provide an outstanding example of the reflection principle in photodissociation with the full nodal structure of the Rydberg state wavefunctions clearly observed in the final Xe+ kinetic energy distributions without the need for scanning the excitation energy. Fitting of the observed distributions provides detailed and precise information on the form of the Xe2+ I(1/2g) potential energy curve involved which is in excellent agreement with the results of photoelectron imaging studies [Shubert and Pratt, J. Chem. Phys. 134, 044315 (2011), 10.1063/1.3533361]. Furthermore, the anisotropy of the product angular distributions yields information on the evolution of the electronic character of the ionic state with internuclear separation, R. The combination of the nature of dissociative ionization and the extent of the bound state wavefunctions provide information over an unusually wide range of internuclear separation R (ΔR > 0.75 Å). This would normally require scanning over a considerable energy region but is obtained in these studies at a fixed excitation energy.

  20. Cosmological model with decaying vacuum energy from quantum mechanics

    NASA Astrophysics Data System (ADS)

    Szydłowski, Marek

    2015-06-01

    We construct the cosmological model to explain the cosmological constant problem. We built the extension of the standard cosmological model Λ CDM by consideration of decaying vacuum energy represented by the running cosmological term. From the principles of quantum mechanics one can find that in the long-term behavior survival probability of unstable states is a decreasing function of the cosmological time and has the inverse powerlike form. This implies that cosmological constant ρvac=Λ (t )=Λbare+α/t2 where Λbare and α are constants. We investigate the dynamics of this model using dynamical system methods due to a link to the Λ (H ) cosmologies. We have found the exact solution for the scale factor as well as the indicators of its variability like the deceleration parameter and the jerk. From the calculation of the jerk we obtain a simple test of the decaying vacuum in the Friedman-Robertson-Walker universe. Using astronomical data [SNIa, H (z ), CMB, BAO] we have estimated the model parameters and compared this model with the Λ CDM model. Our statistical results indicate that the decaying vacuum model is a little worse than the Λ CDM model. But the decaying vacuum cosmological model explains the small value of the cosmological constant today.

  1. Quantum mechanics/molecular mechanics restrained electrostatic potential fitting.

    PubMed

    Burger, Steven K; Schofield, Jeremy; Ayers, Paul W

    2013-12-01

    We present a quantum mechanics/molecular mechanics (QM/MM) method to evaluate the partial charges of amino acid residues for use in MM potentials based on their protein environment. For each residue of interest, the nearby residues are included in the QM system while the rest of the protein is treated at the MM level of theory. After a short structural optimization, the partial charges of the central residue are fit to the electrostatic potential using the restrained electrostatic potential (RESP) method. The resulting charges and electrostatic potential account for the individual environment of the residue, although they lack the transferable nature of library partial charges. To evaluate the quality of the QM/MM RESP charges, thermodynamic integration is used to measure the pKa shift of the aspartic acid residues in three different proteins, turkey egg lysozyme, beta-cryptogein, and Thioredoxin. Compared to the AMBER ff99SB library values, the QM/MM RESP charges show better agreement between the calculated and experimental pK(a) values for almost all of the residues considered.

  2. Physics on the boundary between classical and quantum mechanics

    NASA Astrophysics Data System (ADS)

    't Hooft, Gerard

    2014-04-01

    Nature's laws in the domain where relativistic effects, gravitational effects and quantum effects are all comparatively strong are far from understood. This domain is called the Planck scale. Conceivably, a theory can be constructed where the quantum nature of phenomena at such scales can be attributed to something fundamentally simpler. However, arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there can't be physical laws that require "conspiracy". It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In the lecture we will show several such counterexamples. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. This theory is often portrayed as to underly the quantum field theory of the subatomic particles, including the "Standard Model". So now the question is asked: how can this model feature "conspiracy", and how bad is that? Is there conspiracy in the vacuum fluctuations?

  3. Quantum Mechanics Action of ELF Electromagnetic Fields on Living Organisms

    NASA Astrophysics Data System (ADS)

    Godina-Nava, J. J.

    2010-10-01

    There is presently an intense discussion if extremely low frequency electromagnetic field (ELF-EMF) exposure has consequences for human health. This include exposure to structures and appliances from this range of frequency in the electromagnetic (EM) spectrum. Biological effects of such exposures have been noted frequently, although the implications for specific health effects is not that clear. The basic interactions mechanisms between such fields and living matter is unknown. Numerous hypotheses have been suggested, although none is convincingly supported by experimental data. Various cellular components, processes, and systems can be affected by EMF exposure. Since it is unlikely that EMF can induce DNA damage directly, most studies have examined EMF effects on the cell membrane level, general and specific gene expression, and signal transduction pathways. Even more, a large number of studies have been performed regarding cell proliferation, cell cycle regulation, cell differentiation, metabolism, and various physiological characteristics of cells. The aim of this letter is present the hypothesis of a possible quantum mechanic effect generated by the exposure of ELF EMF, an event which is compatible with the multitude of effects observed after exposure. Based on an extensive literature review, we suggest that ELF EMF exposure is able to perform such activation restructuring the electronic level of occupancy of free radicals in molecules interacting with DNA structures.

  4. Time-dependent {P} {T}-symmetric quantum mechanics

    NASA Astrophysics Data System (ADS)

    Gong, Jiangbin; Wang, Qing-hai

    2013-12-01

    The parity-time-reversal ( {P} {T})-symmetric quantum mechanics (QM) (PTQM) has developed into a noteworthy area of research. However, to date, most known studies of PTQM focused on the spectral properties of non-Hermitian Hamiltonian operators. In this work, we propose an axiom in PTQM in order to study general time-dependent problems in PTQM, e.g., those with a time-dependent {P} {T}-symmetric Hamiltonian and with a time-dependent metric. We illuminate our proposal by examining a proper mapping from a time-dependent Schrödinger-like equation of motion for PTQM to the familiar time-dependent Schrödinger equation in conventional QM. The rich structure of the proper mapping hints that time-dependent PTQM can be a fruitful extension of conventional QM. Under our proposed framework, we further study in detail the Berry-phase generation in a class of {P} {T}-symmetric two-level systems. It is found that a closed path in the parameter space of PTQM is often associated with an open path in a properly mapped problem in conventional QM. In one interesting case, we further interpret the Berry phase as the flux of a continuously tunable fictitious magnetic monopole, thus highlighting the difference between PTQM and conventional QM despite the existence of a proper mapping between them.

  5. Frequency-domain multiscale quantum mechanics/electromagnetics simulation method

    SciTech Connect

    Meng, Lingyi; Yin, Zhenyu; Yam, ChiYung E-mail: ghc@everest.hku.hk; Koo, SiuKong; Chen, GuanHua E-mail: ghc@everest.hku.hk; Chen, Quan; Wong, Ngai

    2013-12-28

    A frequency-domain quantum mechanics and electromagnetics (QM/EM) method is developed. Compared with the time-domain QM/EM method [Meng et al., J. Chem. Theory Comput. 8, 1190–1199 (2012)], the newly developed frequency-domain QM/EM method could effectively capture the dynamic properties of electronic devices over a broader range of operating frequencies. The system is divided into QM and EM regions and solved in a self-consistent manner via updating the boundary conditions at the QM and EM interface. The calculated potential distributions and current densities at the interface are taken as the boundary conditions for the QM and EM calculations, respectively, which facilitate the information exchange between the QM and EM calculations and ensure that the potential, charge, and current distributions are continuous across the QM/EM interface. Via Fourier transformation, the dynamic admittance calculated from the time-domain and frequency-domain QM/EM methods is compared for a carbon nanotube based molecular device.

  6. Indivisibility, Complementarity and Ontology: A Bohrian Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Roldán-Charria, Jairo

    2014-12-01

    The interpretation of quantum mechanics presented in this paper is inspired by two ideas that are fundamental in Bohr's writings: indivisibility and complementarity. Further basic assumptions of the proposed interpretation are completeness, universality and conceptual economy. In the interpretation, decoherence plays a fundamental role for the understanding of measurement. A general and precise conception of complementarity is proposed. It is fundamental in this interpretation to make a distinction between ontological reality, constituted by everything that does not depend at all on the collectivity of human beings, nor on their decisions or limitations, nor on their existence, and empirical reality constituted by everything that not being ontological is, however, intersubjective. According to the proposed interpretation, neither the dynamical properties, nor the constitutive properties of microsystems like mass, charge and spin, are ontological. The properties of macroscopic systems and space-time are also considered to belong to empirical reality. The acceptance of the above mentioned conclusion does not imply a total rejection of the notion of ontological reality. In the paper, utilizing the Aristotelian ideas of general cause and potentiality, a relation between ontological reality and empirical reality is proposed. Some glimpses of ontological reality, in the form of what can be said about it, are finally presented.

  7. Ruling out multi-order interference in quantum mechanics.

    PubMed

    Sinha, Urbasi; Couteau, Christophe; Jennewein, Thomas; Laflamme, Raymond; Weihs, Gregor

    2010-07-23

    Quantum mechanics and gravitation are two pillars of modern physics. Despite their success in describing the physical world around us, they seem to be incompatible theories. There are suggestions that one of these theories must be generalized to achieve unification. For example, Born's rule--one of the axioms of quantum mechanics--could be violated. Born's rule predicts that quantum interference, as shown by a double-slit diffraction experiment, occurs from pairs of paths. A generalized version of quantum mechanics might allow multipath (i.e., higher-order) interference, thus leading to a deviation from the theory. We performed a three-slit experiment with photons and bounded the magnitude of three-path interference to less than 10(-2) of the expected two-path interference, thus ruling out third- and higher-order interference and providing a bound on the accuracy of Born's rule. Our experiment is consistent with the postulate both in semiclassical and quantum regimes.

  8. Optimal state discrimination and unstructured search in nonlinear quantum mechanics

    NASA Astrophysics Data System (ADS)

    Childs, Andrew M.; Young, Joshua

    2016-02-01

    Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics.

  9. A deformation quantization theory for noncommutative quantum mechanics

    SciTech Connect

    Costa Dias, Nuno; Prata, Joao Nuno; Gosson, Maurice de; Luef, Franz

    2010-07-15

    We show that the deformation quantization of noncommutative quantum mechanics previously considered by Dias and Prata ['Weyl-Wigner formulation of noncommutative quantum mechanics', J. Math. Phys. 49, 072101 (2008)] and Bastos, Dias, and Prata ['Wigner measures in non-commutative quantum mechanics', e-print arXiv:math-ph/0907.4438v1; Commun. Math. Phys. (to appear)] can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef ['A new approach to the *-genvalue equation', Lett. Math. Phys. 85, 173-183 (2008)].

  10. Virtual Learning Environment for Interactive Engagement with Advanced Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Pedersen, Mads Kock; Skyum, Birk; Heck, Robert; Müller, Romain; Bason, Mark; Lieberoth, Andreas; Sherson, Jacob F.

    2016-06-01

    A virtual learning environment can engage university students in the learning process in ways that the traditional lectures and lab formats cannot. We present our virtual learning environment StudentResearcher, which incorporates simulations, multiple-choice quizzes, video lectures, and gamification into a learning path for quantum mechanics at the advanced university level. StudentResearcher is built upon the experiences gathered from workshops with the citizen science game Quantum Moves at the high-school and university level, where the games were used extensively to illustrate the basic concepts of quantum mechanics. The first test of this new virtual learning environment was a 2014 course in advanced quantum mechanics at Aarhus University with 47 enrolled students. We found increased learning for the students who were more active on the platform independent of their previous performances.

  11. The Möbius symmetry of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Faraggi, Alon E.; Matone, Marco

    2015-07-01

    The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under D-dimensional Mobius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global Mobius transformations implies that spatial space is compact. Furthermore, it implies energy quantisation and undefinability of quantum trajectories without assuming any prior interpretation of the wave function. The approach may be viewed as conventional quantum mechanics with the caveat that spatial space is compact, as dictated by the Möbius symmetry, with the classical limit corresponding to the decompactification limit. Correspondingly, there exists a finite length scale in the formalism and consequently an intrinsic regularisation scheme. Evidence for the compactness of space may exist in the cosmic microwave background radiation.

  12. Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics

    NASA Astrophysics Data System (ADS)

    Grössing, Gerhard

    2015-10-01

    A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level...

  13. Strong equivalence principle in polymer quantum mechanics and deformed Heisenberg algebra

    NASA Astrophysics Data System (ADS)

    Kajuri, Nirmalya

    2016-10-01

    The strong equivalence principle (SEP) states that the description of a physical system in a gravitational field is indistinguishable from the description of the same system at rest in an accelerating frame. While this statement holds true in both general relativity and ordinary quantum mechanics, one expects it to fail when quantum gravity corrections are taken into account. In this paper we investigate the possible failure of the SEP in two quantum gravity inspired modifications of quantum mechanics—polymer quantum mechanics and deformed Heisenberg algebra. We find that the SEP fails to hold in both these theories. We estimate the deviation from SEP and find in both cases that it is too small to be measured in present day experiments.

  14. Structure/Function Studies of Proteins Using Linear Scaling Quantum Mechanical Methodologies

    SciTech Connect

    Merz, K. M.

    2004-07-19

    We developed a linear-scaling semiempirical quantum mechanical (QM) program (DivCon). Using DivCon we can now routinely carry out calculations at the fully QM level on systems containing up to about 15 thousand atoms. We also implemented a Poisson-Boltzmann (PM) method into DivCon in order to compute solvation free energies and electrostatic properties of macromolecules in solution. This new suite of programs has allowed us to bring the power of quantum mechanics to bear on important biological problems associated with protein folding, drug design and enzyme catalysis. Hence, we have garnered insights into biological systems that have been heretofore impossible to obtain using classical simulation techniques.

  15. Time-dependent perturbation theory in quantum mechanics and the renormalization group

    NASA Astrophysics Data System (ADS)

    Bhattacharjee, J. K.; Ray, D. S.

    2016-06-01

    Time-dependent perturbation theory in quantum mechanics is divergent at long times when the perturbation induces a resonance between two eigenstates of the unperturbed Hamiltonian. Divergences in perturbation theory are also common in quantum field theory and in critical phenomena. The renormalization group (RG) was designed to deal with these divergences. In the last two decades, this procedure has been extended to dynamical systems where the perturbation theory diverges in the long-time limit. In this article, we first review the connection between RG in the context of field theory and RG in the context of dynamical systems. We then show that the long-time divergence in the resonant situation in the time-dependent perturbation theory in quantum mechanics can be removed by using a RG-aided calculational scheme.

  16. The nature of tryptophan radicals involved in the long-range electron transfer of lignin peroxidase and lignin peroxidase-like systems: Insights from quantum mechanical/molecular mechanics simulations.

    PubMed

    Bernini, Caterina; Pogni, Rebecca; Basosi, Riccardo; Sinicropi, Adalgisa

    2012-05-01

    A catalytically active tryptophan radical has been demonstrated to be involved in the long-range electron transfer to the heme cofactor of lignin peroxidase (LiP) from Phanerochaete chrysosporium although no direct detection by EPR spectroscopy of the tryptophan radical intermediate has been reported to date. An engineering-based approach has been used to manipulate the microenvironment of the redox-active tryptophan site in LiP and Coprinus cinereus Peroxidase (CiP), allowing the direct evidence of the tryptophan radical species. In light of the newly available EPR experimental data, we performed a quantum mechanical/molecular mechanics computational study to characterize the tryptophan radicals in the above protein matrices as well as in pristine LiP. The nature of the tryptophan radicals is discussed together with the analysis of their environment with the aim of understanding the different behavior of pristine LiP in comparison with that of LiP and CiP variants.

  17. Quantum-mechanical treatment of an electron undergoing synchrotron radiation.

    NASA Technical Reports Server (NTRS)

    White, D.

    1972-01-01

    The problem of an electron moving perpendicular to an intense magnetic field is approached from the framework of quantum mechanics. A numerical solution to the related rate equations describing the probabilities of occupation of the electron's energy states is put forth along with the expected errors involved. The quantum-mechanical approach is found to predict a significant amount of energy broadening with time for an initially monoenergetic electron beam entering a region of an intense magnetic field as long as the product of initial energy and magnetic field is of order 50 MG BeV or larger.

  18. Spacetime alternatives in the quantum mechanics of a relativistic particle

    SciTech Connect

    Whelan, J.T. Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge, CB3 0EH )

    1994-11-15

    Hartle's generalized quantum mechanics formalism is used to examine spacetime coarse grainings, i.e., sets of alternatives defined with respect to a region extended in time as well as space, in the quantum mechanics of a free relativistic particle. For a simple coarse graining and suitable initial conditions, tractable formulas are found for branch wave functions. Despite the nonlocality of the positive-definite version of the Klein-Gordon inner product, which means that nonoverlapping branches are not sufficient to imply decoherence, some initial conditions are found to give decoherence and allow the consistent assignment of probabilities.

  19. The uncertainty principle determines the nonlocality of quantum mechanics.

    PubMed

    Oppenheim, Jonathan; Wehner, Stephanie

    2010-11-19

    Two central concepts of quantum mechanics are Heisenberg's uncertainty principle and a subtle form of nonlocality that Einstein famously called "spooky action at a distance." These two fundamental features have thus far been distinct concepts. We show that they are inextricably and quantitatively linked: Quantum mechanics cannot be more nonlocal with measurements that respect the uncertainty principle. In fact, the link between uncertainty and nonlocality holds for all physical theories. More specifically, the degree of nonlocality of any theory is determined by two factors: the strength of the uncertainty principle and the strength of a property called "steering," which determines which states can be prepared at one location given a measurement at another.

  20. Constraints on Airy function zeros from quantum-mechanical sum rules

    NASA Astrophysics Data System (ADS)

    Belloni, M.; Robinett, R. W.

    2009-02-01

    We derive new constraints on the zeros of Airy functions by using the so-called quantum bouncer system to evaluate quantum-mechanical sum rules and perform perturbation theory calculations for the Stark effect. Using commutation and completeness relations, we show how to systematically evaluate sums of the form Sp(n) = ∑k≠n1/(ζk - ζn)p, for natural p > 1, where -ζn is the nth zero of Ai(ζ).

  1. Extended supersymmetry and hidden symmetries in one-dimensional matrix quantum mechanics

    NASA Astrophysics Data System (ADS)

    Andrianov, A. A.; Sokolov, A. V.

    2016-01-01

    We study properties of nonlinear supersymmetry algebras realized in the one-dimensional quantum mechanics of matrix systems. Supercharges of these algebras are differential operators of a finite order in derivatives. In special cases, there exist independent supercharges realizing an (extended) supersymmetry of the same super-Hamiltonian. The extended supersymmetry generates hidden symmetries of the super-Hamiltonian. Such symmetries have been found in models with (2×2)-matrix potentials.

  2. Simulation Of Wave Function And Probability Density Of Modified Poschl Teller Potential Derived Using Supersymmetric Quantum Mechanics

    SciTech Connect

    Angraini, Lily Maysari; Suparmi,; Variani, Viska Inda

    2010-12-23

    SUSY quantum mechanics can be applied to solve Schrodinger equation for high dimensional system that can be reduced into one dimensional system and represented in lowering and raising operators. Lowering and raising operators can be obtained using relationship between original Hamiltonian equation and the (super) potential equation. In this paper SUSY quantum mechanics is used as a method to obtain the wave function and the energy level of the Modified Poschl Teller potential. The graph of wave function equation and probability density is simulated by using Delphi 7.0 programming language. Finally, the expectation value of quantum mechanics operator could be calculated analytically using integral form or probability density graph resulted by the programming.

  3. New identities from quantum-mechanical sum rules of parity-related potentials

    NASA Astrophysics Data System (ADS)

    Ayorinde, O. A.; Chisholm, K.; Belloni, M.; Robinett, R. W.

    2010-06-01

    We apply quantum-mechanical sum rules to pairs of one-dimensional systems defined by potential energy functions related by parity. Specifically, we consider symmetric potentials, V(x) = V(- x), and their parity-restricted partners, ones with V(x) but defined only on the positive half-line. We extend recent discussions of sum rules for the quantum bouncer by considering the parity-extended version of this problem, defined by the symmetric linear potential, V(z) = F|z| and find new classes of constraints on the zeros of the Airy function, Ai(ζ), and its derivative, Ai'(ζ). We also consider the parity-restricted version of the harmonic oscillator and find completely new classes of mathematical relations, unrelated to those of the ordinary oscillator problem. These two soluble quantum-mechanical systems defined by power-law potentials provide examples of how the form of the potential (both parity and continuity properties) affects the convergence of quantum-mechanical sum rules. We also discuss semi-classical predictions for expectation values and the Stark effect for these systems.

  4. Comments on continuous observation in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Diósi, L.

    1986-06-01

    It is shown that in open quantum systems the so-called Zeno paradox is not valid. The equations of ideal continuous measurement for Markovian open systems are elaborated and applied to Pauli's simple open system, the actual energy level of which is shown to be monitorable by a continuous nondemolition measurement.

  5. Ground-state properties of the retinal molecule: from quantum mechanical to classical mechanical computations of retinal proteins

    SciTech Connect

    Suhai, Sandor

    2011-01-01

    Retinal proteins are excellent systems for understanding essential physiological processes such as signal transduction and ion pumping. Although the conjugated polyene system of the retinal chromophore is best described with quantum mechanics, simulations of the long-timescale dynamics of a retinal protein in its physiological, flexible, lipid-membrane environment can only be performed at the classical mechanical level. Torsional energy barriers are a critical ingredient of the classical force-field parameters. Here we review briefly current retinal force fields and discuss new quantum mechanical computations to assess how the retinal Schiff base model and the approach used to derive the force-field parameters may influence the torsional potentials.

  6. Chemical dynamics in the gas phase: Time-dependent quantum mechanics of chemical reactions

    SciTech Connect

    Gray, S.K.

    1993-12-01

    A major goal of this research is to obtain an understanding of the molecular reaction dynamics of three and four atom chemical reactions using numerically accurate quantum dynamics. This work involves: (i) the development and/or improvement of accurate quantum mechanical methods for the calculation and analysis of the properties of chemical reactions (e.g., rate constants and product distributions), and (ii) the determination of accurate dynamical results for selected chemical systems, which allow one to compare directly with experiment, determine the reliability of the underlying potential energy surfaces, and test the validity of approximate theories. This research emphasizes the use of recently developed time-dependent quantum mechanical methods, i.e. wave packet methods.

  7. Quantum mechanical modeling the emission pattern and polarization of nanoscale light emitting diodes.

    PubMed

    Wang, Rulin; Zhang, Yu; Bi, Fuzhen; Frauenheim, Thomas; Chen, GuanHua; Yam, ChiYung

    2016-07-21

    Understanding of the electroluminescence (EL) mechanism in optoelectronic devices is imperative for further optimization of their efficiency and effectiveness. Here, a quantum mechanical approach is formulated for modeling the EL processes in nanoscale light emitting diodes (LED). Based on non-equilibrium Green's function quantum transport equations, interactions with the electromagnetic vacuum environment are included to describe electrically driven light emission in the devices. The presented framework is illustrated by numerical simulations of a silicon nanowire LED device. EL spectra of the nanowire device under different bias voltages are obtained and, more importantly, the radiation pattern and polarization of optical emission can be determined using the current approach. This work is an important step forward towards atomistic quantum mechanical modeling of the electrically induced optical response in nanoscale systems.

  8. Water properties from first principles: Simulations by a general-purpose quantum mechanical polarizable force field

    PubMed Central

    Donchev, A. G.; Galkin, N. G.; Illarionov, A. A.; Khoruzhii, O. V.; Olevanov, M. A.; Ozrin, V. D.; Subbotin, M. V.; Tarasov, V. I.

    2006-01-01

    We have recently introduced a quantum mechanical polarizable force field (QMPFF) fitted solely to high-level quantum mechanical data for simulations of biomolecular systems. Here, we present an improved form of the force field, QMPFF2, and apply it to simulations of liquid water. The results of the simulations show excellent agreement with a variety of experimental thermodynamic and structural data, as good or better than that provided by specialized water potentials. In particular, QMPFF2 is the only ab initio force field to accurately reproduce the anomalous temperature dependence of water density to our knowledge. The ability of the same force field to successfully simulate the properties of both organic molecules and water suggests it will be useful for simulations of proteins and protein–ligand interactions in the aqueous environment. PMID:16723394

  9. Quantum mechanical modeling the emission pattern and polarization of nanoscale light emitting diodes

    NASA Astrophysics Data System (ADS)

    Wang, Rulin; Zhang, Yu; Bi, Fuzhen; Frauenheim, Thomas; Chen, Guanhua; Yam, Chiyung

    2016-07-01

    Understanding of the electroluminescence (EL) mechanism in optoelectronic devices is imperative for further optimization of their efficiency and effectiveness. Here, a quantum mechanical approach is formulated for modeling the EL processes in nanoscale light emitting diodes (LED). Based on non-equilibrium Green's function quantum transport equations, interactions with the electromagnetic vacuum environment are included to describe electrically driven light emission in the devices. The presented framework is illustrated by numerical simulations of a silicon nanowire LED device. EL spectra of the nanowire device under different bias voltages are obtained and, more importantly, the radiation pattern and polarization of optical emission can be determined using the current approach. This work is an important step forward towards atomistic quantum mechanical modeling of the electrically induced optical response in nanoscale systems.

  10. Renormalizing the Kinetic Energy Operator in Elementary Quantum Mechanics

    ERIC Educational Resources Information Center

    Coutinho, F. A. B.; Amaku, M.

    2009-01-01

    In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form [psi](r) = u(r)/r, where u(0) [is not equal to] 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly…

  11. Elementary Quantum Mechanics in a High-Energy Process

    ERIC Educational Resources Information Center

    Denville, A.; And Others

    1978-01-01

    Compares two approaches to strong absorption in elementary quantum mechanics; the black sphere and a model based on the continuum theory of nuclear reactions. Examines the application to proton-antiproton interactions at low momenta and concludes that the second model is the appropriate and simplest to use. (Author/GA)

  12. Spin and Uncertainty in the Interpretation of Quantum Mechanics.

    ERIC Educational Resources Information Center

    Hestenes, David

    1979-01-01

    Points out that quantum mechanics interpretations, using Heisenberg's Uncertainty Relations for the position and momentum of an electron, have their drawbacks. The interpretations are limited to the Schrodinger theory and fail to take into account either spin or relativity. Shows why spin cannot be ignored. (Author/GA)

  13. The History of Teaching Quantum Mechanics in Greece

    ERIC Educational Resources Information Center

    Tampakis, Constantin; Skordoulis, Constantin

    2007-01-01

    In this work, our goal is to examine the attitude of the Greek scientific community towards Quantum Mechanics and establish the history of teaching of this theory in Greece. We have examined Physics textbooks written by professors of the University of Athens, as well as records of public speeches, university yearbooks from 1923 to 1970, articles…

  14. Philosophical and metamathematical considerations of quantum mechanical computers

    NASA Astrophysics Data System (ADS)

    Caulfield, H. John; Shamir, Joseph

    1990-07-01

    We ask and give only very preliminary answers to two questions which must arise when we consider quantum mechanical computers with significant quantunt indeterminacy. First, how does this impact our belief in Church's thesis? Second, how does this impact our belief in freedom of thought?

  15. Quantum Mechanics of the Einstein-Hopf Model.

    ERIC Educational Resources Information Center

    Milonni, P. W.

    1981-01-01

    The Einstein-Hopf model for the thermodynamic equilibrium between the electromagnetic field and dipole oscillators is considered within the framework of quantum mechanics. Both the wave and particle aspects of the Einstein fluctuation formula are interpreted in terms of the fundamental absorption and emission processes. (Author/SK)

  16. Hidden algebra method (quasi-exact-solvability in quantum mechanics)

    SciTech Connect

    Turbiner, Alexander

    1996-02-20

    A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.

  17. Completeness of the Coulomb Wave Functions in Quantum Mechanics

    ERIC Educational Resources Information Center

    Mukunda, N.

    1978-01-01

    Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)

  18. Taming the zoo of supersymmetric quantum mechanical models

    NASA Astrophysics Data System (ADS)

    Smilga, A. V.

    2013-05-01

    We show that in many cases nontrivial and complicated supersymmetric quantum mechanical (SQM) models can be obtained from the simple model describing free dynamics in flat complex space by two operations: (i) Hamiltonian reduction and (ii) similarity transformation of the complex supercharges. We conjecture that it is true for any SQM model.

  19. New Potentials for Old: The Darboux Transformation in Quantum Mechanics

    ERIC Educational Resources Information Center

    Williams, Brian Wesley; Celius, Tevye C.

    2008-01-01

    The Darboux transformation in quantum mechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics…

  20. Quantum Mechanics Concept Assessment: Development and Validation Study

    ERIC Educational Resources Information Center

    Sadaghiani, Homeyra R.; Pollock, Steven J.

    2015-01-01

    As part of an ongoing investigation of students' learning in first semester upper-division quantum mechanics, we needed a high-quality conceptual assessment instrument for comparing outcomes of different curricular approaches. The process of developing such a tool started with converting a preliminary version of a 14-item open-ended quantum…

  1. Review of Student Difficulties in Upper-Level Quantum Mechanics

    ERIC Educational Resources Information Center

    Singh, Chandralekha; Marshman, Emily

    2015-01-01

    Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical…

  2. Calendar effects in quantum mechanics in view of interactive holography

    NASA Astrophysics Data System (ADS)

    Berkovich, Simon

    2013-04-01

    Quantum mechanics in terms of interactive holography appears as `normal' science [1]. With the holography quantum behavior is determined by the interplay of material formations and their conjugate images. To begin with, this effortlessly elucidates the nonlocality in quantum entanglements. Then, it has been shown that Schr"odinger's dynamics for a single particle arises from Bi-Fragmental random walks of the particle itself and its holographic image. For many particles this picture blurs with fragments merging as bosons or fermions. In biomolecules, swapping of particles and their holographic placeholders leads to self-replication of the living matter. Because of broad interpretations of quantum formalism direct experiments attributing it to holography may not be very compelling. The holographic mechanism better reveals as an absolute frame of reference. A number of physical and biological events exhibit annual variations when Earth orbital position changes with respect to the universal holographic mechanism. The well established calendar variations of heart attacks can be regarded as a positive outcome of a generalization of the Michelson experiment, where holography is interferometry and ailing hearts are detectors of pathologically replicated proteins. Also, there have been already observed calendar changes in radioactive decay rates. The same could be expected for various fine quantum experiences, like, e.g., Josephson tunneling. In other words, Quantum Mechanics (February) Quantum Mechanics (August). [1] S. Berkovich, ``A comprehensive explanation of quantum mechanics,'' www.cs.gwu.edu/research/technical-report/170 .

  3. Overcoming Misconceptions in Quantum Mechanics with the Time Evolution Operator

    ERIC Educational Resources Information Center

    Quijas, P. C. Garcia; Aguilar, L. M. Arevalo

    2007-01-01

    Recently, there have been many efforts to use the research techniques developed in the field of physics education research to improve the teaching and learning of quantum mechanics. In particular, part of this research is focusing on misconceptions held by students. For instance, a set of misconceptions is associated with the concept of stationary…

  4. Quasi-Hermitian quantum mechanics in phase space

    SciTech Connect

    Curtright, Thomas; Veitia, Andrzej

    2007-10-15

    We investigate quasi-Hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact results are easily obtained. We emphasize spatially periodic solutions, compute various distribution functions and phase-space metrics, and explore the relationships between them.

  5. Exactly Solvable Quantum Mechanical Potentials: An Alternative Approach.

    ERIC Educational Resources Information Center

    Pronchik, Jeremy N.; Williams, Brian W.

    2003-01-01

    Describes an alternative approach to finding exactly solvable, one-dimensional quantum mechanical potentials. Differs from the usual approach in that instead of starting with a particular potential and seeking solutions to the related Schrodinger equations, it begins with known solutions to second-order ordinary differential equations and seeks to…

  6. Topology of optimally controlled quantum mechanical transition probability landscapes

    SciTech Connect

    Rabitz, H.; Ho, T.-S.; Hsieh, M.; Kosut, R.; Demiralp, M.

    2006-07-15

    An optimally controlled quantum system possesses a search landscape defined by the physical objective as a functional of the control field. This paper particularly explores the topological structure of quantum mechanical transition probability landscapes. The quantum system is assumed to be controllable and the analysis is based on the Euler-Lagrange variational equations derived from a cost function only requiring extremizing the transition probability. It is shown that the latter variational equations are automatically satisfied as a mathematical identity for control fields that either produce transition probabilities of zero or unit value. Similarly, the variational equations are shown to be inconsistent (i.e., they have no solution) for any control field that produces a transition probability different from either of these two extreme values. An upper bound is shown to exist on the norm of the functional derivative of the transition probability with respect to the control field anywhere over the landscape. The trace of the Hessian, evaluated for a control field producing a transition probability of a unit value, is shown to be bounded from below. Furthermore, the Hessian at a transition probability of unit value is shown to have an extensive null space and only a finite number of negative eigenvalues. Collectively, these findings show that (a) the transition probability landscape extrema consists of values corresponding to no control or full control, (b) approaching full control involves climbing a gentle slope with no false traps in the control space and (c) an inherent degree of robustness exists around any full control solution. Although full controllability may not exist in some applications, the analysis provides a basis to understand the evident ease of finding controls that produce excellent yields in simulations and in the laboratory.

  7. Free Energies of Chemical Reactions in Solution and in Enzymes with Ab Initio Quantum Mechanics/Molecular Mechanics Methods

    NASA Astrophysics Data System (ADS)

    Hu, Hao; Yang, Weitao

    2008-05-01

    Combined quantum mechanics/molecular mechanics (QM/MM) methods provide an accurate and efficient energetic description of complex chemical and biological systems, leading to significant advances in the understanding of chemical reactions in solution and in enzymes. Here we review progress in QM/MM methodology and applications, focusing on ab initio QM-based approaches. Ab initio QM/MM methods capitalize on the accuracy and reliability of the associated quantum-mechanical approaches, however, at a much higher computational cost compared with semiempirical quantum-mechanical approaches. Thus reaction-path and activation free-energy calculations based on ab initio QM/MM methods encounter unique challenges in simulation timescales and phase-space sampling. This review features recent developments overcoming these challenges and enabling accurate free-energy determination for reaction processes in solution and in enzymes, along with applications.

  8. Free energies of chemical reactions in solution and in enzymes with ab initio quantum mechanics/molecular mechanics methods.

    PubMed

    Hu, Hao; Yang, Weitao

    2008-01-01

    Combined quantum mechanics/molecular mechanics (QM/MM) methods provide an accurate and efficient energetic description of complex chemical and biological systems, leading to significant advances in the understanding of chemical reactions in solution and in enzymes. Here we review progress in QM/MM methodology and applications, focusing on ab initio QM-based approaches. Ab initio QM/MM methods capitalize on the accuracy and reliability of the associated quantum-mechanical approaches, however, at a much higher computational cost compared with semiempirical quantum-mechanical approaches. Thus reaction-path and activation free-energy calculations based on ab initio QM/MM methods encounter unique challenges in simulation timescales and phase-space sampling. This review features recent developments overcoming these challenges and enabling accurate free-energy determination for reaction processes in solution and in enzymes, along with applications.

  9. Quantum mechanics concept assessment: Development and validation study

    NASA Astrophysics Data System (ADS)

    Sadaghiani, Homeyra R.; Pollock, Steven J.

    2015-06-01

    As part of an ongoing investigation of students' learning in first semester upper-division quantum mechanics, we needed a high-quality conceptual assessment instrument for comparing outcomes of different curricular approaches. The process of developing such a tool started with converting a preliminary version of a 14-item open-ended quantum mechanics assessment tool (QMAT) to a multiple-choice (MC) format. Further question refinement, development of effective distractors, adding new questions, and robust statistical analysis has led to a 31-item quantum mechanics concept assessment (QMCA) test. The QMCA is used as post-test only to assess students' knowledge about five main topics of quantum measurement: the time-independent Schrödinger equation, wave functions and boundary conditions, time evolution, and probability density. During two years of testing and refinement, the QMCA has been given in alpha (N =61 ) and beta versions (N =263 ) to students in upper division quantum mechanics courses at 11 different institutions with an average post-test score of 54%. By allowing for comparisons of student learning across different populations and institutions, the QMCA provides instructors and researchers a more standard measure of effectiveness of different curricula or teaching strategies on student conceptual understanding of quantum mechanics. In this paper, we discuss the construction of effective distractors and the use of student interviews and expert feedback to revise and validate both questions and distractors. We include the results of common statistical tests of reliability and validity, which suggest the instrument is presently in a stable, usable, and promising form.

  10. Scattering problems in the fractional quantum mechanics governed by the 2D space-fractional Schrödinger equation

    SciTech Connect

    Dong, Jianping

    2014-03-15

    The 2D space-fractional Schrödinger equation in the time-independent and time-dependent cases for the scattering problems in the fractional quantum mechanics is studied. We define the Green's functions for the two cases and give the mathematical expression of them in infinite series form and in terms of some special functions. The asymptotic formulas of the Green's functions are also given, and applied to get the approximate wave functions for the fractional quantum scattering problems. These results contain those in the standard (integer) quantum mechanics as special cases, and can be applied to study the complex quantum systems.

  11. The Heisenberg-Weyl algebra on the circle and a related quantum mechanical model for hindered rotation.

    PubMed

    Kouri, Donald J; Markovich, Thomas; Maxwell, Nicholas; Bodmann, Bernhard G

    2009-07-01

    We discuss a periodic variant of the Heisenberg-Weyl algebra, associated with the group of translations and modulations on the circle. Our study of uncertainty minimizers leads to a periodic version of canonical coherent states. Unlike the canonical, Cartesian case, there are states for which the uncertainty product associated with the generators of the algebra vanishes. Next, we explore the supersymmetric (SUSY) quantum mechanical setting for the uncertainty-minimizing states and interpret them as leading to a family of "hindered rotors". Finally, we present a standard quantum mechanical treatment of one of these hindered rotor systems, including numerically generated eigenstates and energies.

  12. Whitehead's Philosophy and Quantum Mechanics (QM)

    NASA Astrophysics Data System (ADS)

    Malin, Shimon

    This paper is a tribute to Abner Shimony and a continuation of my discussions with him. In the first part some ofWhitehead's concepts, and, in particular, actual entities and atemporal processes, are introduced. These are shown to correspond to the objectivized aspects of the collapse of quantum states. Next we reconcile the entanglement of quantum states with the speed of light barrier for the transmission of information by modifying Whitehead's system: We suggest that events that take place far apart can be aspects if the same actual entity. We show that this takes care of Lovejoy's objection to Whitehead's system.

  13. Chaos as a Bridge between Determinism and Probability in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    McHarris, Wm. C.

    Quantum mechanics is fundamentally a probabilistic science, whereas classical mechanics is deterministic. This dichotomy has led to numerous disputes and confusion, ranging from the Einstein-Bohr debates of the 1930's [Einstein, Podolsky, and Rosen 1935; Bohr 1935], through attempts to establish determinism in quantum mechanics by means of introducing "hidden variables" [de Broglie 1960, de Broglie 1964; Bohm 1952], to lengthy discussions of epistemological versus ontological interpretations of quantum mechanics [Bohm and Hiley 1993]. Throughout most of the twentieth century the Copenhagen interpretation of Bohr and Heisenberg has endured as the orthodox interpretation, replete with contradictions and paradoxes such as duality, the necessity for an observer before a quantum system can attain physical meaning, and the reduction of the wave function upon observation. The reductio ad absurdum of such paradoxes was the example of Schrödinger's cat [Schrödinger 1936; Gribben 1984, Gribben 1995], in which a cat inside a closed chamber remained in limbo as a linear superposition of -dead cat> +-live cat> until an observer determined whether or not a radioactive nucleus had decayed, releasing a deadly poison.

  14. Derivation of quantum mechanics from a single fundamental modification of the relations between physical properties

    NASA Astrophysics Data System (ADS)

    Hofmann, Holger F.

    2014-04-01

    Recent results obtained in quantum measurements indicate that the fundamental relations between three physical properties of a system can be represented by complex conditional probabilities. Here, it is shown that these relations provide a fully deterministic and universally valid framework on which all of quantum mechanics can be based. Specifically, quantum mechanics can be derived by combining the rules of Bayesian probability theory with only a single additional law that explains the phases of complex probabilities. This law, which I introduce here as the law of quantum ergodicity, is based on the observation that the reality of physical properties cannot be separated from the dynamics by which they emerge in measurement interactions. The complex phases are an expression of this inseparability and represent the dynamical structure of transformations between the different properties. In its quantitative form, the law of quantum ergodicity describes a fundamental relation between the ergodic probabilities obtained by dynamical averaging and the deterministic relations between three properties expressed by the complex conditional probabilities. The complete formalism of quantum mechanics can be derived from this one relation, without any axiomatic mathematical assumptions about state vectors or superpositions. It is therefore possible to explain all quantum phenomena as the consequence of a single fundamental law of physics.

  15. Analysis of ice-binding sites in fish type II antifreeze protein by quantum mechanics.

    PubMed Central

    Cheng, Yuhua; Yang, Zuoyin; Tan, Hongwei; Liu, Ruozhuang; Chen, Guangju; Jia, Zongchao

    2002-01-01

    Many organisms living in cold environments can survive subzero temperatures by producing antifreeze proteins (AFPs) or antifreeze glycoproteins. In this paper we investigate the ice-binding surface of type II AFP by quantum mechanical methods, which, to the best of our knowledge, represents the first time that molecular orbital computational approaches have been applied to AFPs. Molecular mechanical approaches, including molecular docking, energy minimization, and molecular dynamics simulation, were used to obtain optimal systems for subsequent quantum mechanical analysis. We selected 17 surface patches covering the entire surface of the type II AFP and evaluated the interaction energy between each of these patches and two different ice planes using semi-empirical quantum mechanical methods. We have demonstrated the weak orbital overlay phenomenon and the change of bond orders in ice. These results consistently indicate that a surface patch containing 19 residues (K37, L38, Y20, E22, Y21, I19, L57, T56, F53, M127, T128, F129, R17, C7, N6, P5, G10, Q1, and W11) is the most favorable ice-binding site for both a regular ice plane and an ice plane where water O atoms are randomly positioned. Furthermore, for the first time the computation results provide new insights into the weakening of the ice lattice upon AFP binding, which may well be a primary factor leading to AFP-induced ice growth inhibition. PMID:12324437

  16. Classical and Quantum-Mechanical State Reconstruction

    ERIC Educational Resources Information Center

    Khanna, F. C.; Mello, P. A.; Revzen, M.

    2012-01-01

    The aim of this paper is to present the subject of state reconstruction in classical and in quantum physics, a subject that deals with the experimentally acquired information that allows the determination of the physical state of a system. Our first purpose is to explain a method for retrieving a classical state in phase space, similar to that…

  17. Quantum mechanical model in gravity theory

    NASA Astrophysics Data System (ADS)

    Losyakov, V. V.

    2016-05-01

    We consider a model of a real massive scalar field defined as homogeneous on a d-dimensional sphere such that the sphere radius, time scale, and scalar field are related by the equations of the general theory of relativity. We quantize this system with three degrees of freedom, define the observables, and find dynamical mean values of observables in the regime where the scalar field mass is much less than the Planck mass.

  18. Explicit polarization: a quantum mechanical framework for developing next generation force fields.

    PubMed

    Gao, Jiali; Truhlar, Donald G; Wang, Yingjie; Mazack, Michael J M; Löffler, Patrick; Provorse, Makenzie R; Rehak, Pavel

    2014-09-16

    Conspectus Molecular mechanical force fields have been successfully used to model condensed-phase and biological systems for a half century. By means of careful parametrization, such classical force fields can be used to provide useful interpretations of experimental findings and predictions of certain properties. Yet, there is a need to further improve computational accuracy for the quantitative prediction of biomolecular interactions and to model properties that depend on the wave functions and not just the energy terms. A new strategy called explicit polarization (X-Pol) has been developed to construct the potential energy surface and wave functions for macromolecular and liquid-phase simulations on the basis of quantum mechanics rather than only using quantum mechanical results to fit analytic force fields. In this spirit, this approach is called a quantum mechanical force field (QMFF). X-Pol is a general fragment method for electronic structure calculations based on the partition of a condensed-phase or macromolecular system into subsystems ("fragments") to achieve computational efficiency. Here, intrafragment energy and the mutual electronic polarization of interfragment interactions are treated explicitly using quantum mechanics. X-Pol can be used as a general, multilevel electronic structure model for macromolecular systems, and it can also serve as a new-generation force field. As a quantum chemical model, a variational many-body (VMB) expansion approach is used to systematically improve interfragment interactions, including exchange repulsion, charge delocalization, dispersion, and other correlation energies. As a quantum mechanical force field, these energy terms are approximated by empirical functions in the spirit of conventional molecular mechanics. This Account first reviews the formulation of X-Pol, in the full variationally correct version, in the faster embedded version, and with systematic many-body improvements. We discuss illustrative examples

  19. Explicit Polarization: A Quantum Mechanical Framework for Developing Next Generation Force Fields

    PubMed Central

    2015-01-01

    Conspectus Molecular mechanical force fields have been successfully used to model condensed-phase and biological systems for a half century. By means of careful parametrization, such classical force fields can be used to provide useful interpretations of experimental findings and predictions of certain properties. Yet, there is a need to further improve computational accuracy for the quantitative prediction of biomolecular interactions and to model properties that depend on the wave functions and not just the energy terms. A new strategy called explicit polarization (X-Pol) has been developed to construct the potential energy surface and wave functions for macromolecular and liquid-phase simulations on the basis of quantum mechanics rather than only using quantum mechanical results to fit analytic force fields. In this spirit, this approach is called a quantum mechanical force field (QMFF). X-Pol is a general fragment method for electronic structure calculations based on the partition of a condensed-phase or macromolecular system into subsystems (“fragments”) to achieve computational efficiency. Here, intrafragment energy and the mutual electronic polarization of interfragment interactions are treated explicitly using quantum mechanics. X-Pol can be used as a general, multilevel electronic structure model for macromolecular systems, and it can also serve as a new-generation force field. As a quantum chemical model, a variational many-body (VMB) expansion approach is used to systematically improve interfragment interactions, including exchange repulsion, charge delocalization, dispersion, and other correlation energies. As a quantum mechanical force field, these energy terms are approximated by empirical functions in the spirit of conventional molecular mechanics. This Account first reviews the formulation of X-Pol, in the full variationally correct version, in the faster embedded version, and with systematic many-body improvements. We discuss illustrative

  20. Explicit polarization: a quantum mechanical framework for developing next generation force fields.

    PubMed

    Gao, Jiali; Truhlar, Donald G; Wang, Yingjie; Mazack, Michael J M; Löffler, Patrick; Provorse, Makenzie R; Rehak, Pavel

    2014-09-16

    Conspectus Molecular mechanical force fields have been successfully used to model condensed-phase and biological systems for a half century. By means of careful parametrization, such classical force fields can be used to provide useful interpretations of experimental findings and predictions of certain properties. Yet, there is a need to further improve computational accuracy for the quantitative prediction of biomolecular interactions and to model properties that depend on the wave functions and not just the energy terms. A new strategy called explicit polarization (X-Pol) has been developed to construct the potential energy surface and wave functions for macromolecular and liquid-phase simulations on the basis of quantum mechanics rather than only using quantum mechanical results to fit analytic force fields. In this spirit, this approach is called a quantum mechanical force field (QMFF). X-Pol is a general fragment method for electronic structure calculations based on the partition of a condensed-phase or macromolecular system into subsystems ("fragments") to achieve computational efficiency. Here, intrafragment energy and the mutual electronic polarization of interfragment interactions are treated explicitly using quantum mechanics. X-Pol can be used as a general, multilevel electronic structure model for macromolecular systems, and it can also serve as a new-generation force field. As a quantum chemical model, a variational many-body (VMB) expansion approach is used to systematically improve interfragment interactions, including exchange repulsion, charge delocalization, dispersion, and other correlation energies. As a quantum mechanical force field, these energy terms are approximated by empirical functions in the spirit of conventional molecular mechanics. This Account first reviews the formulation of X-Pol, in the full variationally correct version, in the faster embedded version, and with systematic many-body improvements. We discuss illustrative examples

  1. Multilayered model in optics and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Kovalev, M. D.

    2009-08-01

    Three types of dispersion equations are analyzed that describe the eigenvalues of the effective refractive index of a multilayer plane optical waveguide and the energy eigenvalues of a quantum particle placed in a piecewise constant potential field. The first equation (D1) is derived by setting to zero the determinant of the system of linear equations produced by matching the solutions in the layers. The second equation (D2) is obtained using the well-known method of characteristic matrices. The third equation has been obtained in the general case by the author and is known as a multilayer equation. Simple relations between the three equations are established. It is shown that the set of roots of D2 exactly coincides with the set of eigenvalues of the multilayer problem, while the roots of D1 and the multilayer equation contain those equal to the refractive index in the optical case (or to the potential in the quantum case) in internal layers of the system, which may be superfluous. Examples are presented.

  2. Universal edge information from wavefunction deformation

    NASA Astrophysics Data System (ADS)

    Ho, Wen Wei; Cincio, Lukasz; Moradi, Heidar; Vidal, Guifre

    It is well known that the bulk physics of a topological phase constrains its possible edge physics through the bulk-edge correspondence. Therefore, the different types of edge theories that a topological phase can host is a universal piece of data which can be used to characterize topological order. Here, we argue that beginning from only the fixed point wavefunction (FPW) of a nonchiral topological phase and by locally deforming it, all possible edge theories can be extracted from its entanglement Hamiltonian (EH). We illustrate our claim by deforming the FPW of the Wen-plaquette model, the quantum double of ℤ2. We show that the possible EHs of the deformed FPWs reflect the known possible types of edge theories, which are generically gapped, but gapless if translational symmetry is preserved. We stress that our results do not require an underlying Hamiltonian - thus, this lends support to the notion that a topological phase is indeed characterized by only a set of quantum states and can be studied through its FPWs. Also affiliated to Perimeter Inst for Theo Phys.

  3. Accurate basis set truncation for wavefunction embedding

    NASA Astrophysics Data System (ADS)

    Barnes, Taylor A.; Goodpaster, Jason D.; Manby, Frederick R.; Miller, Thomas F.

    2013-07-01

    Density functional theory (DFT) provides a formally exact framework for performing embedded subsystem electronic structure calculations, including DFT-in-DFT and wavefunction theory-in-DFT descriptions. In the interest of efficiency, it is desirable to truncate the atomic orbital basis set in which the subsystem calculation is performed, thus avoiding high-order scaling with respect to the size of the MO virtual space. In this study, we extend a recently introduced projection-based embedding method [F. R. Manby, M. Stella, J. D. Goodpaster, and T. F. Miller III, J. Chem. Theory Comput. 8, 2564 (2012)], 10.1021/ct300544e to allow for the systematic and accurate truncation of the embedded subsystem basis set. The approach is applied to both covalently and non-covalently bound test cases, including water clusters and polypeptide chains, and it is demonstrated that errors associated with basis set truncation are controllable to well within chemical accuracy. Furthermore, we show that this approach allows for switching between accurate projection-based embedding and DFT embedding with approximate kinetic energy (KE) functionals; in this sense, the approach provides a means of systematically improving upon the use of approximate KE functionals in DFT embedding.

  4. Saddle point localization of molecular wavefunctions

    NASA Astrophysics Data System (ADS)

    Mellau, Georg Ch.; Kyuberis, Alexandra A.; Polyansky, Oleg L.; Zobov, Nikolai; Field, Robert W.

    2016-09-01

    The quantum mechanical description of isomerization is based on bound eigenstates of the molecular potential energy surface. For the near-minimum regions there is a textbook-based relationship between the potential and eigenenergies. Here we show how the saddle point region that connects the two minima is encoded in the eigenstates of the model quartic potential and in the energy levels of the [H, C, N] potential energy surface. We model the spacing of the eigenenergies with the energy dependent classical oscillation frequency decreasing to zero at the saddle point. The eigenstates with the smallest spacing are localized at the saddle point. The analysis of the HCN ↔ HNC isomerization states shows that the eigenstates with small energy spacing relative to the effective (v1, v3, ℓ) bending potentials are highly localized in the bending coordinate at the transition state. These spectroscopically detectable states represent a chemical marker of the transition state in the eigenenergy spectrum. The method developed here provides a basis for modeling characteristic patterns in the eigenenergy spectrum of bound states.

  5. Saddle point localization of molecular wavefunctions

    PubMed Central

    Mellau, Georg Ch.; Kyuberis, Alexandra A.; Polyansky, Oleg L.; Zobov, Nikolai; Field, Robert W.

    2016-01-01

    The quantum mechanical description of isomerization is based on bound eigenstates of the molecular potential energy surface. For the near-minimum regions there is a textbook-based relationship between the potential and eigenenergies. Here we show how the saddle point region that connects the two minima is encoded in the eigenstates of the model quartic potential and in the energy levels of the [H, C, N] potential energy surface. We model the spacing of the eigenenergies with the energy dependent classical oscillation frequency decreasing to zero at the saddle point. The eigenstates with the smallest spacing are localized at the saddle point. The analysis of the HCN ↔ HNC isomerization states shows that the eigenstates with small energy spacing relative to the effective (v1, v3, ℓ) bending potentials are highly localized in the bending coordinate at the transition state. These spectroscopically detectable states represent a chemical marker of the transition state in the eigenenergy spectrum. The method developed here provides a basis for modeling characteristic patterns in the eigenenergy spectrum of bound states. PMID:27629262

  6. Saddle point localization of molecular wavefunctions.

    PubMed

    Mellau, Georg Ch; Kyuberis, Alexandra A; Polyansky, Oleg L; Zobov, Nikolai; Field, Robert W

    2016-01-01

    The quantum mechanical description of isomerization is based on bound eigenstates of the molecular potential energy surface. For the near-minimum regions there is a textbook-based relationship between the potential and eigenenergies. Here we show how the saddle point region that connects the two minima is encoded in the eigenstates of the model quartic potential and in the energy levels of the [H, C, N] potential energy surface. We model the spacing of the eigenenergies with the energy dependent classical oscillation frequency decreasing to zero at the saddle point. The eigenstates with the smallest spacing are localized at the saddle point. The analysis of the HCN ↔ HNC isomerization states shows that the eigenstates with small energy spacing relative to the effective (v1, v3, ℓ) bending potentials are highly localized in the bending coordinate at the transition state. These spectroscopically detectable states represent a chemical marker of the transition state in the eigenenergy spectrum. The method developed here provides a basis for modeling characteristic patterns in the eigenenergy spectrum of bound states. PMID:27629262

  7. A modified Lax-Phillips scattering theory for quantum mechanics

    NASA Astrophysics Data System (ADS)

    Strauss, Y.

    2015-07-01

    The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.

  8. Probability in the Many-Worlds Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Vaidman, Lev

    It is argued that, although in the Many-Worlds Interpretation of quantum mechanics there is no "probability" for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: (a) A "sleeping pill" gedanken experiment which makes correspondence between an illegitimate question: "What is the probability of an outcome of a quantum measurement?" with a legitimate question: "What is the probability that `I' am in the world corresponding to that outcome?"; (b) A gedanken experiment which splits the world into several worlds which are identical according to some symmetry condition; and (c) Relativistic causality, which together with (b) explain the Born rule of standard quantum mechanics. The Quantum Sleeping Beauty controversy and "caring measure" replacing probability measure are discussed.

  9. A modified Lax-Phillips scattering theory for quantum mechanics

    SciTech Connect

    Strauss, Y.

    2015-07-15

    The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.

  10. Wavefunction collapse through backaction of counting weakly interacting photons

    NASA Astrophysics Data System (ADS)

    Harrell, L. E.

    2016-03-01

    We apply the formalism of quantum measurement theory to the idealized measurement of the position of a particle with an optical interferometer, finding that the backaction of counting entangled photons systematically collapses the particle's wavefunction toward a narrow Gaussian wavepacket at the location xest determined by the measurement without appeal to environmental decoherence or other spontaneous collapse mechanism. Further, the variance in the particle's position, as calculated from the post-measurement wavefunction, agrees precisely with shot-noise limited uncertainty of the measured xest. Both the identification of the absolute square of the particle's initial wavefunction as the probability density for xest and the de Broglie hypothesis emerge as consequences of interpreting the intensity of the optical field as proportional to the probability of detecting a photon. Linear momentum information that is encoded in the particle's initial wavefunction survives the measurement, and the pre-measurement expectation values are preserved in the ensemble average.

  11. Hidden algebra method (quasi-exact-solvability in quantum mechanics)

    SciTech Connect

    Turbiner, A. |

    1996-02-01

    A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland {ital N}-body problems ass ociated with an existence of the hidden algebra {ital sl}{sub {ital N}} is discussed extensively. {copyright} {ital 1996 American Institute of Physics.}

  12. Resolution of the Klein Paradox within Relativistic Quantum Mechanics

    SciTech Connect

    Alhaidari, A. D.

    2011-10-27

    We present a resolution of the Klein paradox within the framework of one-particle relativistic quantum mechanics (no pair production). Not only reflection becomes total but the vacuum remains neutral as well. This is accomplished by replacing the pair production process with virtual negative energy ''incidence'' within the barrier in a process analogous to the introduction of image charges in electrostatic and virtual sources in optics.

  13. Quantum mechanical reality according to Copenhagen 2.0

    NASA Astrophysics Data System (ADS)

    Din, Allan M.

    2016-05-01

    The long-standing conceptual controversies concerning the interpretation of nonrelativistic quantum mechanics are argued, on one hand, to be due to its incompleteness, as affirmed by Einstein. But on the other hand, it appears to be possible to complete it at least partially, as Bohr might have appreciated it, in the framework of its standard mathematical formalism with observables as appropriately defined self-adjoint operators. This completion of quantum mechanics is based on the requirement on laboratory physics to be effectively confined to a bounded space region and on the application of the von Neumann deficiency theorem to properly define a set of self-adjoint extensions of standard observables, e.g. the momenta and the Hamiltonian, in terms of certain isometries on the region boundary. This is formalized mathematically in the setting of a boundary ontology for the so-called Qbox in which the wave function acquires a supplementary dependence on a set of Additional Boundary Variables (ABV). It is argued that a certain geometric subset of the ABV parametrizing Quasi-Periodic Translational Isometries (QPTI) has a particular physical importance by allowing for the definition of an ontic wave function, which has the property of epitomizing the spatial wave function “collapse.” Concomitantly the standard wave function in an unbounded geometry is interpreted as an epistemic wave function, which together with the ontic QPTI wave function gives rise to the notion of two-wave duality, replacing the standard concept of wave-particle duality. More generally, this approach to quantum physics in a bounded geometry provides a novel analytical basis for a better understanding of several conceptual notions of quantum mechanics, including reality, nonlocality, entanglement and Heisenberg’s uncertainty relation. The scope of this analysis may be seen as a foundational update of the multiple versions 1.x of the Copenhagen interpretation of quantum mechanics, which is

  14. An approximate approach to quantum mechanical study of biomacromolecules

    NASA Astrophysics Data System (ADS)

    Chen, Xihua

    This thesis summarizes the author's major work in Prof. John Z.H. Zhang's Threoretical Chemistry research group. In Chapter 1, we present a general description of MFCC (molecular fractionation with conjugated caps) method that has been developed in this group to treat biomacromolecules in a divide-and-conquer fashion. Then we give in detail a computational study of MFCC application to peptide/protein that contains disulfide bonds. Continued on the basis of previous MFCC tests, this study provides another numerical support for the accuracy of the MFCC approach to full quantum mechanical calculation of protein/peptide-small molecule interaction. In Chapter 2, we further develop the MFCC scheme for quantum mechanical computation of DNA-ligand interaction energy. We study three oligonuclear acid interaction systems: dinucleotide dCG/water, trinucleotide dCGT/water and a Watson-Crick paired DNA segment dCGT/dGCA. The MFCC interaction energies are found to be in excellent agreement with the corresponding results obtained from the full system ab initio calculations. This study is an exemplification of the application of the general MFCC approach to biomacromolecules. In Chapter 3, firstly, a MFCC-downhill simplex method is proposed to study binding structures of ligands (atoms, ions, or small molecules) in large molecular complex systems. This method employs the MFCC approach to compute the interaction energy-structure relation of the system and implements the downhill simplex algorithm for structural optimization. Secondly, this method is numerically tested on a system of [KCp(18-crown-6)], as a simplest monatomic case study, to optimize the binding position of the potassium cation in a fixed coordination Cp and 18-crown-6 coordinating sphere. The result of the MFCC-downhill simplex optimization shows good agreement with both the crystal structure and with the full-system downhill simplex optimized structure. The effects of the initial structure of the simplex and of the

  15. A perspective on quantum mechanics calculations in ADMET predictions.

    PubMed

    Bowen, J Phillip; Güner, Osman F

    2013-01-01

    Understanding the molecular basis of drug action has been an important objective for pharmaceutical scientists. With the increasing speed of computers and the implementation of quantum chemistry methodologies, pharmacodynamic and pharmacokinetic problems have become more computationally tractable. Historically the former has been the focus of drug design, but within the last two decades efforts to understand the latter have increased. It takes about fifteen years and over $1 billion dollars for a drug to go from laboratory hit, through lead optimization, to final approval by the U.S. Food and Drug Administration. While the costs have increased substantially, the overall clinical success rate for a compound to emerge from clinical trials is approximately 10%. Most of the attrition rate can be traced to ADMET (absorption, distribution, metabolism, excretion, and toxicity) problems, which is a powerful impetus to study these issues at an earlier stage in drug discovery. Quantum mechanics offers pharmaceutical scientists the opportunity to investigate pharmacokinetic problems at the molecular level prior to laboratory preparation and testing. This review will provide a perspective on the use of quantum mechanics or a combination of quantum mechanics coupled with other classical methods in the pharmacokinetic phase of drug discovery. A brief overview of the essential features of theory will be discussed, and a few carefully selected examples will be given to highlight the computational methods.

  16. Foundations of a spacetime path formalism for relativistic quantum mechanics

    SciTech Connect

    Seidewitz, Ed

    2006-11-15

    Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative first-quantized formulation can be given for relativistic quantum mechanics, based on the parametrized paths of particles in spacetime. Because time is treated similarly to the three space coordinates, rather than as an evolution parameter, such a spacetime approach has proved particularly useful in the study of quantum gravity and cosmology. This paper shows how a spacetime path formalism can be considered to arise naturally from the fundamental principles of the Born probability rule, superposition, and Poincare invariance. The resulting formalism can be seen as a foundation for a number of previous parametrized approaches in the literature, relating, in particular, 'off-shell' theories to traditional on-shell quantum field theory. It reproduces the results of perturbative quantum field theory for free and interacting particles, but provides intriguing possibilities for a natural program for regularization and renormalization. Further, an important consequence of the formalism is that a clear probabilistic interpretation can be maintained throughout, with a natural reduction to nonrelativistic quantum mechanics.

  17. Investigations of fundamental phenomena in quantum mechanics with neutrons

    NASA Astrophysics Data System (ADS)

    Hasegawa, Yuji

    2014-04-01

    Neutron interferometer and polarimeter are used for the experimental investigations of quantum mechanical phenomena. Interferometry exhibits clear evidence of quantum-contextuality and polarimetry demonstrates conflicts of a contextual model of quantum mechanics á la Leggett. In these experiments, entanglements are achieved between degrees of freedom in a single-particle: spin, path and energy degrees of freedom are manipulated coherently and entangled. Both experiments manifest the fact that quantum contextuality is valid for phenomena with matter waves with high precision. In addition, another experiment is described which deals with error-disturbance uncertainty relation: we have experimentally tested error-disturbance uncertainty relations, one is derived by Heisenberg and the other by Ozawa. Experimental results confirm the fact that the Heisenberg's uncertainty relation is often violated and that the new relation by Ozawa is always larger than the limit. At last, as an example of a counterfactual phenomenon of quantum mechanics, observation of so-called quantum Cheshire Cat is carried out by using neutron interferometer. Experimental results suggest that pre- and post-selected neutrons travel through one of the arms of the interferometer while their magnetic moment is located in the other arm.

  18. Wave-function functionals for the density

    SciTech Connect

    Slamet, Marlina; Pan Xiaoyin; Sahni, Viraht

    2011-11-15

    We extend the idea of the constrained-search variational method for the construction of wave-function functionals {psi}[{chi}] of functions {chi}. The search is constrained to those functions {chi} such that {psi}[{chi}] reproduces the density {rho}(r) while simultaneously leading to an upper bound to the energy. The functionals are thereby normalized and automatically satisfy the electron-nucleus coalescence condition. The functionals {psi}[{chi}] are also constructed to satisfy the electron-electron coalescence condition. The method is applied to the ground state of the helium atom to construct functionals {psi}[{chi}] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle operators W={Sigma}{sub i}r{sub i}{sup n}, n=-2,-1,1,2, W={Sigma}{sub i}{delta}(r{sub i}) are exact, as must be the case. The expectations of the kinetic energy operator W=-(1/2){Sigma}{sub i}{nabla}{sub i}{sup 2}, the two-particle operators W={Sigma}{sub n}u{sup n}, n=-2,-1,1,2, where u=|r{sub i}-r{sub j}|, and the energy are accurate. We note that the construction of such functionals {psi}[{chi}] is an application of the Levy-Lieb constrained-search definition of density functional theory. It is thereby possible to rigorously determine which functional {psi}[{chi}] is closer to the true wave function.

  19. Inferring the statistical interpretation of quantum mechanics from the classical limit

    PubMed

    Gottfried

    2000-06-01

    It is widely believed that the statistical interpretation of quantum mechanics cannot be inferred from the Schrodinger equation itself, and must be stated as an additional independent axiom. Here I propose that the situation is not so stark. For systems that have both continuous and discrete degrees of freedom (such as coordinates and spin respectively), the statistical interpretation for the discrete variables is implied by requiring that the system's gross motion can be classically described under circumstances specified by the Schrodinger equation. However, this is not a full-fledged derivation of the statistical interpretation because it does not apply to the continuous variables of classical mechanics.

  20. A tractable prescription for large-scale free flight expansion of wavefunctions

    NASA Astrophysics Data System (ADS)

    Deuar, P.

    2016-11-01

    A numerical recipe is given for obtaining the density image of an initially compact quantum mechanical wavefunction that has expanded by a large but finite factor under free flight. The recipe given avoids the memory storage problems that plague this type of calculation by reducing the problem to the sum of a number of fast Fourier transforms carried out on the relatively small initial lattice. The final expanded state is given exactly on a coarser magnified grid with the same number of points as the initial state. An important application of this technique is the simulation of measured time-of-flight images in ultracold atom experiments, especially when the initial clouds contain superfluid defects. It is shown that such a finite-time expansion, rather than a far-field approximation is essential to correctly predict images of defect-laden clouds, even for long flight times. Examples shown are: an expanding quasicondensate with soliton defects and a matter-wave interferometer in 3D.

  1. The GRW Theory and Vagueness in Quantum Mechanics.

    NASA Astrophysics Data System (ADS)

    Lewis, Peter John

    This dissertation is an investigation into the adequacy of the GRW theory of quantum mechanics as a solution to the measurement problem, and a comparison between the GRW theory and the other potential solutions. A new problem, the vagueness problem, is found to afflict a broad class of quantum mechanical theories, including the GRW theory. The standard theory of quantum mechanics and the measurement problem from which it suffers are sketched. The GRW theory of quantum mechanics is explained, along with how it is intended to solve the measurement problem. The major obstacle to the adequacy of the GRW theory in this regard, known as the tails problem, is presented. Two potential lines of response to the tails problem are outlined, namely modifying the GRW dynamics and modifying the interpretation rule connecting the language of the theory to everyday language. The first of these is quickly shown to be unworkable. The second is investigated in some detail. A defense of this line of response in terms of the inherent vagueness of the translation between the language of physical theory and everyday language is presented. However, it is argued that any modified interpretation rule which can adequately respond to the tails problem will violate intuitions concerning counting and the logic of parts and wholes. This is termed the vagueness problem. The extent of the vagueness problem among the other promising solutions to the measurement problem is investigated. It is demonstrated that the modal theories suffer from this problem, but Bohm-type hidden variable theories do not. It is argued that this gives us reason to prefer the hidden variable theories over their competitors. The empirical adequacy of the GRW theory is investigated. It is found that empirical considerations cannot at present decide between the GRW theory and its alternatives, although they may be able to do so eventually. The conclusion drawn is that because of the vagueness problem, the GRW theory and the

  2. Quantum mechanical theory of dynamic nuclear polarization in solid dielectrics

    PubMed Central

    Hu, Kan-Nian; Debelouchina, Galia T.; Smith, Albert A.; Griffin, Robert G.

    2011-01-01

    Microwave driven dynamic nuclear polarization (DNP) is a process in which the large polarization present in an electron spin reservoir is transferred to nuclei, thereby enhancing NMR signal intensities. In solid dielectrics there are three mechanisms that mediate this transfer—the solid effect (SE), the cross effect (CE), and thermal mixing (TM). Historically these mechanisms have been discussed theoretically using thermodynamic parameters and average spin interactions. However, the SE and the CE can also be modeled quantum mechanically with a system consisting of a small number of spins and the results provide a foundation for the calculations involving TM. In the case of the SE, a single electron–nuclear spin pair is sufficient to explain the polarization mechanism, while the CE requires participation of two electrons and a nuclear spin, and can be used to understand the improved DNP enhancements observed using biradical polarizing agents. Calculations establish the relations among the electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) frequencies and the microwave irradiation frequency that must be satisfied for polarization transfer via the SE or the CE. In particular, if δ, Δ < ω0I, where δ and Δ are the homogeneous linewidth and inhomogeneous breadth of the EPR spectrum, respectively, we verify that the SE occurs when ωM = ω0S ± ω0I, where ωM, ω0S and ω0I are, respectively, the microwave, and the EPR and NMR frequencies. Alternatively, when Δ > ω0I > δ, the CE dominates the polarization transfer. This two-electron process is optimized when ω0S1−ω0S2=ω0I and ωM∼ω0S1 orω0S2, where ω0S1 and ω0S2 are the EPR Larmor frequencies of the two electrons. Using these matching conditions, we calculate the evolution of the density operator from electron Zeeman order to nuclear Zeeman order for both the SE and the CE. The results provide insights into the influence of the microwave irradiation field, the

  3. The impact of QCD and light-cone quantum mechanics on nuclear physics

    SciTech Connect

    Brodsky, S.J.; Schlumpf, F.

    1994-12-01

    We discuss a number of novel applications of Quantum Chromodynamics to nuclear structure and dynamics, such as the reduced amplitude formalism for exclusive nuclear amplitudes. We particularly emphasize the importance of light-cone Hamiltonian and Fock State methods as a tool for describing the wavefunctions of composite relativistic many-body systems and their interactions. We also show that the use of covariant kinematics leads to nontrivial corrections to the standard formulae for the axial, magnetic, and quadrupole moments of nucleons and nuclei.

  4. Chemical dynamics in the gas phase : quantum mechanics of chemical reactions.

    SciTech Connect

    Gray, S. K.

    2006-01-01

    This research program focuses on both the development and application of accurate quantum mechanical methods to describe gas phase chemical reactions and highly excited molecules. Emphasis is often placed on time-dependent or integrative approaches that, in addition to computational simplifications, yield useful mechanistic insights. Applications to systems of current experimental and theoretical interest are emphasized. The results of these calculations also allow one to gauge the quality of the underlying potential energy surfaces and the reliability of more approximate theoretical approaches such as classical trajectories and transition state theories.

  5. An interpretation within philosophy of the relationship between classical mechanics and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Sibelius, Patrick

    1989-11-01

    A mapping of a finite directed graph onto a curve in space-time is considered. The mapping induces the dynamics of a free particle moving along the curve. The distinction between the Lagrangian and the Hamiltonian formulation of particle mechanics is expressed in terms of the distinction between referring to a particle in space and time and referring to the points in space which the particle occupies, respectively. These elements are combined to yield an interpretation of Feynman's path integral formulation of quantum mechanics. Describing a bound state of a system as a particle is discussed.

  6. Reply to "Comment on 'Similarity between quantum mechanics and thermodynamics: Entropy, temperature, and Carnot cycle' ''.

    PubMed

    Abe, Sumiyoshi

    2015-05-01

    In their Comment on the paper [Abe and Okuyama, Phys. Rev. E 83, 021121 (2011)], González-Díaz and Díaz-Solórzano discuss that the initial state of the quantum-mechanical analog of the Carnot cycle should be not in a pure state but in a mixed state due to a projective measurement of the system energy. Here, first the Comment is shown to miss the point. Then, second, multiple projective measurements are discussed as a generalization of the Comment, although they are not relevant to the work commented.

  7. Sine-Gordon quantum mechanics on the complex plane and N=2 gauge theory

    SciTech Connect

    He Wei

    2010-05-15

    We study the relation between the N=2 gauge theory in the {Omega} background and the quantized integral system recently proposed by Nekrasov and Shatashvili. We focus on the simplest case, the pure Yang-Mills theory with the SU(2) gauge group and the corresponding sine-Gordon integral model on the complex plane. We analyze the periodic wave function and the corresponding energy spectrum of the sine-Gordon quantum mechanics, and find this model contains information of the low energy effective theory of the gauge theory.

  8. Quantum-mechanical derivation of the Davydov equations for multi-quanta states

    SciTech Connect

    Kerr, W.C.; Lomdahl, P.S.

    1989-01-01

    Our purpose here is to present a derivation of the Davydov equations which employs only quantum-mechanical techniques. The derivation here is more general than our previous treatment of this problem because we use an Ansatz which has present several quanta of the high frequency oscillator system rather than just one quantum. Since some steps of the calculation are the same as those in our paper which treats the single quantum case, reference will be made to that paper for some of the those details. 9 refs.

  9. Quantum mechanical algebraic variational methods for inelastic and reactive molecular collisions

    NASA Technical Reports Server (NTRS)

    Schwenke, David W.; Haug, Kenneth; Zhao, Meishan; Truhlar, Donald G.; Sun, Yan

    1988-01-01

    The quantum mechanical problem of reactive or nonreactive scattering of atoms and molecules is formulated in terms of square-integrable basis sets with variational expressions for the reactance matrix. Several formulations involving expansions of the wave function (the Schwinger variational principle) or amplitude density (a generalization of the Newton variational principle), single-channel or multichannel distortion potentials, and primitive or contracted basis functions are presented and tested. The test results, for inelastic and reactive atom-diatom collisions, suggest that the methods may be useful for a variety of collision calculations and may allow the accurate quantal treatment of systems for which other available methods would be prohibitively expensive.

  10. Quantum Mechanics for Everyone: Can it be done with Technology?

    NASA Astrophysics Data System (ADS)

    Zollman, Dean

    2004-10-01

    The Visual Quantum Mechanics project has created a series of teaching/learning units to introduce quantum physics to a variety of audiences ranging from high school students who normally would not study these topics to undergraduate physics majors. Most recently we have been developing materials relating modern medical procedures and contemporary physics. In all of these materials interactive computer visualizations are coupled with hands-on experiences to create a series of activities which help students learn about some aspects of quantum mechanics. Our goal is to enable students to obtain a qualitative and, where appropriate, a quantitative understanding of contemporary ideas in physics. Included in the instructional materials are student-centered activities that address a variety of concepts in quantum physics and applications to devices such as the light emitting diode, the electron microscope, an inexpensive infrared detection card, and the Star Trek Transporter. Whenever possible the students begin the study of a new concept with an experiment using inexpensive equipment. They, then, build models of the physical phenomenon using interactive computer visualization and conclude by applying those models to new situations. For physics students these visualizations are usually followed by a mathematical approach. For others the visualizations provide a framework for understanding the concepts. Thus, Visual Quantum Mechanics allows a wide range of students to begin to understand the basic concepts, implications and interpretations of quantum physics. At present we are building on this foundation to create materials which show the connection between contemporary physics and modern medical diagnosis. Additional information is available at http://web.phys.ksu.edu/.

  11. Quantum Mechanics and Perceptive Processes: A Reply to Elio Conte

    NASA Astrophysics Data System (ADS)

    Ghirardi, GianCarlo

    2015-07-01

    Recently, Elio Conte has commented a paper by the present author devoted to analyze the possibility of checking experimentally whether the perceptual process can lead to the collapse of the wavefunction. Here we answer to the comments by Conte and we show that he has missed to grasp the crucial elements of our proposal. Morever, we discuss some ideas put forward by Conte concerning the occurrence of quantum superpositions of different states of consciousness and we show that they are rather vague and not cogent.

  12. Some thoughts about consciousness: from a quantum mechanics perspective.

    PubMed

    Gargiulo, Gerald J

    2013-08-01

    The article explores some of the basic findings of quantum physics and information theory and their possible usefulness in offering new vistas for understanding psychoanalysis and the patient-analyst interchange. Technical terms are explained and placed in context, and examples of applying quantum models to clinical experience are offered. Given the complexity of the findings of quantum mechanics and information theory, the article aims only to introduce some of the major concepts from these disciplines. Within this framework the article also briefly addresses the question of mind as well as the problematic of reducing the experience of consciousness to neurological brain functioning.

  13. Generalized Uncertainty Relation in the Non-commutative Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Chung, Won Sang

    2016-06-01

    In this paper the non-commutative quantum mechanics (NCQM) with the generalized uncertainty relations {Δ } x1 {Δ } x2 ≥ {θ}/{2}, {Δ} p1 {Δ } p2 ≥ {bar{θ}}/{2}, {Δ } xi {Δ } pi ≥ {hbar _{eff}}/{2} is discussed. Four each uncertainty relation, wave functions saturating each uncertainty relation are explicitly constructed. The unitary operators relating the non-commutative position and momentum operators to the commutative position and momentum operators are also investigated. We also discuss the uncertainty relation related to the harmonic oscillator.

  14. Quantum mechanical calculation of Rydberg–Rydberg autoionization rates

    NASA Astrophysics Data System (ADS)

    Kiffner, Martin; Ceresoli, Davide; Li, Wenhui; Jaksch, Dieter

    2016-10-01

    We present quantum mechanical calculations of autoionization rates for two rubidium Rydberg atoms with weakly overlapping electron clouds. We neglect exchange effects and consider tensor products of independent atom states forming an approximate basis of the two-electron state space. We consider large sets of two-atom states with randomly chosen quantum numbers and find that the charge overlap between the two Rydberg electrons allows one to characterise the magnitude of the autoionization rates. If the electron clouds overlap by more than one percent, the autoionization rates increase approximately exponentially with the charge overlap. This finding is independent of the energy of the initial state.

  15. Sachdev-Ye-Kitaev model as Liouville quantum mechanics

    NASA Astrophysics Data System (ADS)

    Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex

    2016-10-01

    We show that the proper inclusion of soft reparameterization modes in the Sachdev-Ye-Kitaev model of N randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics. As a result, all zero temperature correlation functions decay with the universal exponent ∝τ - 3 / 2 for times larger than the inverse single particle level spacing τ ≫ Nln ⁡ N. In the particular case of the single particle Green function this behavior is manifestation of the zero-bias anomaly, or scaling in energy as ɛ 1 / 2. We also present exact diagonalization study supporting our conclusions.

  16. On the quantum mechanical solutions with minimal length uncertainty

    NASA Astrophysics Data System (ADS)

    Shababi, Homa; Pedram, Pouria; Chung, Won Sang

    2016-06-01

    In this paper, we study two generalized uncertainty principles (GUPs) including [X,P] = iℏ(1 + βP2j) and [X,P] = iℏ(1 + βP2 + kβ2P4) which imply minimal measurable lengths. Using two momentum representations, for the former GUP, we find eigenvalues and eigenfunctions of the free particle and the harmonic oscillator in terms of generalized trigonometric functions. Also, for the latter GUP, we obtain quantum mechanical solutions of a particle in a box and harmonic oscillator. Finally we investigate the statistical properties of the harmonic oscillator including partition function, internal energy, and heat capacity in the context of the first GUP.

  17. New type of N = 4 supersymmetric quantum mechanics

    SciTech Connect

    Ivanov, Evgeny; Sidorov, Stepan

    2014-07-23

    We overview a new type of supersymmetric quantum mechanics models based on the worldline realizations of the supergroup SU(2|1). Our main focus is on the models associated with the chiral multiplets (2,4,2). Considering two nonequivalent deformations of the standard N = 4, d = 1 superspace, we define the relevant chiral superfields and construct their SU(2|1) invariant actions. We give off- and on-shell descriptions of these models and perform their quantization. The basic peculiarities of such models and interrelations between them are briefly discussed.

  18. Foundations of Quantum Mechanics: recent developments at INRIM

    SciTech Connect

    Genovese, Marco; Piacentini, Fabrizio

    2011-09-23

    This paper's purpose is to show some experiments performed in the 'Carlo Novero' labs of the Optics Division of the National Institute of Metrological Research (INRIM, Torino, Italy) in the last years, aiming to discriminate between Standard Quantum Mechanics and some specific, restricted class of Hidden Variable Theories (HVTs).The first experiment, realized in two different configurations, will perform the Alicki - Van Ryn non-classicality test on single particles, in our specific case heralded single photons. The second experiment instead will be on the testing of two restricted Local Realistic Theories (LRTs), properly built to describe polarization entangled photons experiments, whose inequalities are not affected by the detection loophole.

  19. Experimental testing of quantum mechanical predictions of mutagenicity: aminopyrazoles.

    PubMed

    Leach, Andrew G; McCoull, William; Bailey, Andrew; Barton, Peter; Mee, Christine; Rosevere, Eleanor

    2013-05-20

    A computational method for predicting the likelihood of aromatic amines being active in the Ames test for mutagenicity was trialed on a set of aminopyrazoles. A virtual array of compounds was generated from the available sets of hydrazines and α-cyanoaldehydes (or ketones) and quantum mechanical calculations used to compute a probability of being active in the Ames test. The compounds selected for synthesis and testing were not based on the predictions and so spanned the range of predicted probabilities. The subsequently generated results of the Ames test were in good correspondence with the predictions and confirm this approach as a useful means of predicting likely mutagenic risk. PMID:23541044

  20. Mathematical foundations of quantum mechanics: An advanced short course

    NASA Astrophysics Data System (ADS)

    Moretti, Valter

    2016-08-01

    This paper collects and extends the lectures I gave at the “XXIV International Fall Workshop on Geometry and Physics” held in Zaragoza (Spain) during September 2015. Within these lectures I review the formulation of Quantum Mechanics, and quantum theories in general, from a mathematically advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions, discussing some fundamental ideas, mathematical tools and theorems also related to the representation of physical symmetries. The final step consists of an elementary introduction the so-called (C∗-) algebraic formulation of quantum theories.

  1. The extension problem for partial Boolean structures in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Budroni, Costantino; Morchio, Giovanni

    2010-12-01

    Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back to Bell and Kochen-Specker. An algebraic approach is presented, allowing for a discussion of partial classical extension, amounting to reduction of the "number of contexts," classical representability arising as a special case. As a result, known techniques are generalized and some of the associated computational difficulties overcome. The implications on the discussion of Boole-Bell inequalities are indicated.

  2. The Quasi-Exactly Solvable Problems in Relativistic Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Liu, Li-Yan; Hao, Qing-Hai

    2014-06-01

    We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein—Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the general form of the potential, we present several examples to give the specific forms. In the examples, we show for special parameters the harmonic potential plus Coulomb potential, Killingbeck potential and a quartic potential plus Cornell potential are quasi-exactly solvable potentials.

  3. Minimum length from quantum mechanics and classical general relativity.

    PubMed

    Calmet, Xavier; Graesser, Michael; Hsu, Stephen D H

    2004-11-19

    We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length lP. This suggests a Planck-size minimum ball of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball. Nevertheless, we deduce a fundamental limit on their accuracy of order lP. Our results imply a device independent limit on possible position measurements.

  4. Point form relativistic quantum mechanics and relativistic SU(6)

    NASA Technical Reports Server (NTRS)

    Klink, W. H.

    1993-01-01

    The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.

  5. Importance of parametrizing constraints in quantum-mechanical variational calculations

    NASA Technical Reports Server (NTRS)

    Chung, Kwong T.; Bhatia, A. K.

    1992-01-01

    In variational calculations of quantum mechanics, constraints are sometimes imposed explicitly on the wave function. These constraints, which are deduced by physical arguments, are often not uniquely defined. In this work, the advantage of parametrizing constraints and letting the variational principle determine the best possible constraint for the problem is pointed out. Examples are carried out to show the surprising effectiveness of the variational method if constraints are parameterized. It is also shown that misleading results may be obtained if a constraint is not parameterized.

  6. A finite Zitterbewegung model for relativistic quantum mechanics

    SciTech Connect

    Noyes, H.P.

    1990-02-19

    Starting from steps of length h/mc and time intervals h/mc{sup 2}, which imply a quasi-local Zitterbewegung with velocity steps {plus minus}c, we employ discrimination between bit-strings of finite length to construct a necessary 3+1 dimensional event-space for relativistic quantum mechanics. By using the combinatorial hierarchy to label the strings, we provide a successful start on constructing the coupling constants and mass ratios implied by the scheme. Agreement with experiments is surprisingly accurate. 22 refs., 1 fig.

  7. Equations of motion in general relativity and quantum mechanics

    NASA Astrophysics Data System (ADS)

    O'Hara, Paul

    2011-12-01

    In a previous article a relationship was established between the linearized metrics of General Relativity associated with geodesics and the Dirac Equation of quantum mechanics. In this paper the extension of that result to arbitrary curves is investigated. A generalized Dirac equation is derived and shown to be related to the Lie derivative of the momentum along the curve. In addition,the equations of motion are derived from the Hamilton-Jacobi equation associated with the metric and the wave equation associated with the Hamiltonian is then shown not to commute with the Dirac operator. Finally, the Maxwell-Boltzmann distribution is shown to be a consequence of geodesic motion.

  8. Localization properties in one-dimensional disordered supersymmetric quantum mechanics

    SciTech Connect

    Comtet, A.; Desbois, J.; Monthus, C. |

    1995-05-01

    A model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics is considered. The case where the superpotential {phi}({ital x}) is a random telegraph process is solved exactly. Both the localization length and the density of states are obtained analytically. A detailed study of the low energy behaviour is presented. Analytical and numerical results are presented in the case where the intervals over which {phi}({ital x}) is kept constant are distributed according to a broad distribution. Various applications of this model are considered. {copyright} 1995 Academic Press, Inc.

  9. Np Incorporation into Uranyl Alteration Phases: A Quantum Mechanical Approach

    SciTech Connect

    Shuller, Lindsay; Ewing, Rodney C. |; Becker, Udo

    2007-07-01

    Neptunium is a major contributor to the long-term radioactivity in a geologic repository for spent nuclear fuel (SNF) due to its long half-life (2.1 million years). The mobility of Np may be decreased by its incorporation into the U{sup 6+} phases that form during the corrosion of SNF. The ionic radii of Np{sup 5+} (0.089 nm) and U{sup 6+} (0.087 nm) are similar, as is their chemistry. Experimental studies have shown that Np can be incorporated into uranyl phases up to concentrations on the order of 100 ppm. The low concentration of Np in the uranyl phases complicates experimental detection and presents a significant challenge for determining the incorporation mechanism. Therefore, we have used quantum mechanical calculations to investigate incorporation mechanisms and evaluate the energetics of Np substituting for U. CASTEP, a density functional theory based code that uses plane waves to model the behavior of the valence electrons and pseudo-potentials to model the behavior of the core and inner valence electrons, was used to calculate optimal H positions, relaxed geometry, and the energy of different uranyl phases. The incorporation energy for Np into uranyl alteration phases was calculated for studtite, [(UO{sub 2})O{sub 2}(H{sub 2}O){sub 2}](H{sub 2}O){sub 2}, and boltwoodite, HK(UO{sub 2})(SiO{sub 4}) 1.5(H{sub 2}O). Studtite is the rare case of a stable, naturally-occurring peroxide mineral, in this case a uranyl hydroxyl peroxide that forms in the presence of H{sub 2}O{sub 2} from the radiolysis of H{sub 2}O. For studtite, two incorporation mechanisms were evaluated: (1) charge-balanced substitution of Np{sup 5+} and H{sup +} for one U{sup 6+}, and (2) direct substitution of Np{sup 6+} for U{sup 6+}. For boltwoodite, the H atomic positions prior to Np incorporation were determined, as well as the Np incorporation mechanisms and the corresponding substitution energies. The preferential incorporation of Np into different structure types of U{sup 6+} minerals

  10. Quantum mechanical and experimental analyses of TNT metabolite 2-hydroxylamino-4,6-dinitrotoluene

    NASA Astrophysics Data System (ADS)

    Junk, Thomas; Liu, Yuemin; Li, Zhong; Perkins, Richard; Liu, Yucheng

    2015-01-01

    In this study, a combined quantum mechanical and experimental analyses were performed to investigate crystal structure of the immediate degradation product of TNT, 2-hydroxylamino-4,6-dinitrotoluene (2-HADNT) and to reveal its important chemical properties. Leakage of 2-HADNT has caused serious environmental pollution and therefore raises widespread concerns. In the quantum mechanical analysis, the B3LYP/6-311+G**, B3LYP/aug-c-pVDZ, M06HF/aug-cc-pVDZ, and MP2/aug-cc-pVDZ methods were employed for geometrical optimization and single point calculations of chemical properties of the compound. Such properties include highest unoccupied molecular orbitals (HOMO) - lowest occupied molecular orbitals (LUMO) separation, dipole moment, atomization energy, and vibrational frequencies. Experimental analysis and validation showed that the energy minimized structures acquired from the quantum mechanical analysis were very similar to those obtained by X-ray crystallography. The 6-NO2 groups twist out of plane with respect to the benzene ring in both the crystallographic and energy minimized structures. The 4-NO2 group exhibits co-planarity with the phenyl ring in both the crystallographic and energy minimized structures as well. Unlike TNT, however, the energy barrier to orthogonal conformation is only 3.8 kcal/mol. In addition, considerable discrepancies between results obtained from the MP2 and B3LYP methods were observed, which suggest that it has to be very careful when applying B3LYP method to study such class of compounds. Through this study, a more accurate description of the chemical properties of dispersion-dominated aromatic systems was acquired. The chemical properties found from this study can help researchers to better understand the compound of 2-HADNT and to develop effective management plans for such compound so as to minimize its impact on the environment.

  11. Comparative role of potential structure in classical, semiclassical, and quantum mechanics

    SciTech Connect

    Judson, R.S.; Shi, S.; Rabitz, H.

    1989-02-15

    The corresponding effects of features in the potential on classical, semiclassical, and quantum mechanics are probed using the technique of functional sensitivity analysis. It is shown that the classical and quantum functional sensitivities are equivalent in the classical (small (h/2..pi..)) and harmonic limits. Classical and quantum mechanics are known to react in qualitatively similar ways provided that features on the potential are smooth on the length scale of oscillations in the quantum wave function. By using functional sensitivity analysis, we are able to show in detail how the classical and quantum dynamics differ in the way that they sense the potential. Two examples are given, the first of which is the harmonic oscillator. This problem is well understood by other means but is useful to examine because it illustrates the detailed information about the interaction of the potential and the dynamics which can be provided by functional sensitivity analysis, simplifying the analysis of more complex systems. The second example is the collinear H+H/sub 2/ reaction. In that case there are a number of detailed and striking differences between the ways that classical and quantum mechanics react to features on the potential. For features which are broad compared to oscillations in the wave function, the two react in qualitatively the same way. The sensitivities are oscillatory, however, and there are phasing differences between the classical and quantum sensitivity functions. This means that using classical mechanics plus experimental data in an inversion scheme intended to find the ''true'' potential will necessarily introduce sizeable errors.

  12. Quantum mechanics of excitation transport in photosynthetic complexes: a key issues review.

    PubMed

    Levi, Federico; Mostarda, Stefano; Rao, Francesco; Mintert, Florian

    2015-07-01

    For a long time microscopic physical descriptions of biological processes have been based on quantum mechanical concepts and tools, and routinely employed by chemical physicists and quantum chemists. However, the last ten years have witnessed new developments on these studies from a different perspective, rooted in the framework of quantum information theory. The process that more, than others, has been subject of intense research is the transfer of excitation energy in photosynthetic light-harvesting complexes, a consequence of the unexpected experimental discovery of oscillating signals in such highly noisy systems. The fundamental interdisciplinary nature of this research makes it extremely fascinating, but can also constitute an obstacle to its advance. Here in this review our objective is to provide an essential summary of the progress made in the theoretical description of excitation energy dynamics in photosynthetic systems from a quantum mechanical perspective, with the goal of unifying the language employed by the different communities. This is initially realized through a stepwise presentation of the fundamental building blocks used to model excitation transfer, including protein dynamics and the theory of open quantum system. Afterwards, we shall review how these models have evolved as a consequence of experimental discoveries; this will lead us to present the numerical techniques that have been introduced to quantitatively describe photo-absorbed energy dynamics. Finally, we shall discuss which mechanisms have been proposed to explain the unusual coherent nature of excitation transport and what insights have been gathered so far on the potential functional role of such quantum features.

  13. Quantum mechanics of excitation transport in photosynthetic complexes: a key issues review

    NASA Astrophysics Data System (ADS)

    Levi, Federico; Mostarda, Stefano; Rao, Francesco; Mintert, Florian

    2015-07-01

    For a long time microscopic physical descriptions of biological processes have been based on quantum mechanical concepts and tools, and routinely employed by chemical physicists and quantum chemists. However, the last ten years have witnessed new developments on these studies from a different perspective, rooted in the framework of quantum information theory. The process that more, than others, has been subject of intense research is the transfer of excitation energy in photosynthetic light-harvesting complexes, a consequence of the unexpected experimental discovery of oscillating signals in such highly noisy systems. The fundamental interdisciplinary nature of this research makes it extremely fascinating, but can also constitute an obstacle to its advance. Here in this review our objective is to provide an essential summary of the progress made in the theoretical description of excitation energy dynamics in photosynthetic systems from a quantum mechanical perspective, with the goal of unifying the language employed by the different communities. This is initially realized through a stepwise presentation of the fundamental building blocks used to model excitation transfer, including protein dynamics and the theory of open quantum system. Afterwards, we shall review how these models have evolved as a consequence of experimental discoveries; this will lead us to present the numerical techniques that have been introduced to quantitatively describe photo-absorbed energy dynamics. Finally, we shall discuss which mechanisms have been proposed to explain the unusual coherent nature of excitation transport and what insights have been gathered so far on the potential functional role of such quantum features.

  14. Quantum mechanics of excitation transport in photosynthetic complexes: a key issues review.

    PubMed

    Levi, Federico; Mostarda, Stefano; Rao, Francesco; Mintert, Florian

    2015-07-01

    For a long time microscopic physical descriptions of biological processes have been based on quantum mechanical concepts and tools, and routinely employed by chemical physicists and quantum chemists. However, the last ten years have witnessed new developments on these studies from a different perspective, rooted in the framework of quantum information theory. The process that more, than others, has been subject of intense research is the transfer of excitation energy in photosynthetic light-harvesting complexes, a consequence of the unexpected experimental discovery of oscillating signals in such highly noisy systems. The fundamental interdisciplinary nature of this research makes it extremely fascinating, but can also constitute an obstacle to its advance. Here in this review our objective is to provide an essential summary of the progress made in the theoretical description of excitation energy dynamics in photosynthetic systems from a quantum mechanical perspective, with the goal of unifying the language employed by the different communities. This is initially realized through a stepwise presentation of the fundamental building blocks used to model excitation transfer, including protein dynamics and the theory of open quantum system. Afterwards, we shall review how these models have evolved as a consequence of experimental discoveries; this will lead us to present the numerical techniques that have been introduced to quantitatively describe photo-absorbed energy dynamics. Finally, we shall discuss which mechanisms have been proposed to explain the unusual coherent nature of excitation transport and what insights have been gathered so far on the potential functional role of such quantum features. PMID:26194028

  15. Comparison between the Morse eigenfunctions and deformed oscillator wavefunctions

    SciTech Connect

    Recamier, J.; Mochan, W. L.; Gorayeb, M.; Paz, J. L.

    2008-04-15

    In this work we introduce deformed creation and annihilation operators which differ from the usual harmonic oscillator operators a, a{sup {dagger}} by a number operator function A circumflex = a circumflex f(n circumflex ), A circumflex {sup {dagger}} = f(n circumflex )a circumflex {sup {dagger}}. We construct the deformed coordinate and momentum in terms of the deformed operators and maintain only up to first order terms in the deformed operators. By application of the deformed annihilation operator upon the vacuum state we get the ground state wavefunction in the configuration space and the wavefunctions for excited states are obtained by repeated application of the deformed creation operator. Finally, we compare the wavefunctions obtained with the deformed operators with the corresponding Morse eigenfunctions.

  16. Exact and Optimal Quantum Mechanics/Molecular Mechanics Boundaries.

    PubMed

    Sun, Qiming; Chan, Garnet Kin-Lic

    2014-09-01

    Motivated by recent work in density matrix embedding theory, we define exact link orbitals that capture all quantum mechanical (QM) effects across arbitrary quantum mechanics/molecular mechanics (QM/MM) boundaries. Exact link orbitals are rigorously defined from the full QM solution, and their number is equal to the number of orbitals in the primary QM region. Truncating the exact set yields a smaller set of link orbitals optimal with respect to reproducing the primary region density matrix. We use the optimal link orbitals to obtain insight into the limits of QM/MM boundary treatments. We further analyze the popular general hybrid orbital (GHO) QM/MM boundary across a test suite of molecules. We find that GHOs are often good proxies for the most important optimal link orbital, although there is little detailed correlation between the detailed GHO composition and optimal link orbital valence weights. The optimal theory shows that anions and cations cannot be described by a single link orbital. However, expanding to include the second most important optimal link orbital in the boundary recovers an accurate description. The second optimal link orbital takes the chemically intuitive form of a donor or acceptor orbital for charge redistribution, suggesting that optimal link orbitals can be used as interpretative tools for electron transfer. We further find that two optimal link orbitals are also sufficient for boundaries that cut across double bonds. Finally, we suggest how to construct "approximately" optimal link orbitals for practical QM/MM calculations.

  17. Reality in quantum mechanics, Extended Everett Concept, and consciousness

    NASA Astrophysics Data System (ADS)

    Mensky, M. B.

    2007-09-01

    Conceptual problems in quantum mechanics result from the specific quantum concept of reality and require, for their solution, including the observer’s consciousness into the quantum theory of measurements. Most naturally, this is achieved in the framework of Everett’s “many-world interpretation” of quantum mechanics. According to this interpretation, various classical alternatives are perceived by consciousness separately from each other. In the Extended Everett Concept (EEC) proposed by the present author, the separation of the alternatives is identified with the phenomenon of consciousness. This explains the classical character of the alternatives and unusual manifestations of consciousness arising “at the edge of consciousness” (i.e., in sleep or trance) when its access to “other alternative classical realities” (other Everett’s worlds) becomes feasible. Because of reversibility of quantum evolution in EEC, all time moments in the quantum world are equivalent, while the impression of flow of time appears only in consciousness. If it is assumed that consciousness may influence the probabilities of alternatives (which is consistent in case of infinitely many Everett’s worlds), EEC explains free will, “probabilistic miracles” (observing low-probability events), and decreasing entropy in the sphere of life.

  18. Implications of Einstein-Weyl Causality on Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Bendaniel, David

    A fundamental physical principle that has consequences for the topology of space-time is the principle of Einstein-Weyl causality. This also has quantum mechanical manifestations. Borchers and Sen have rigorously investigated the mathematical implications of Einstein-Weyl causality and shown the denumerable space-time Q2 would be implied. They were left with important philosophical paradoxes regarding the nature of the physical real line E, e.g., whether E = R, the real line of mathematics. In order to remove these paradoxes an investigation into a constructible foundation is suggested. We have pursued such a program and find it indeed provides a dense, denumerable space-time and, moreover, an interesting connection with quantum mechanics. We first show that this constructible theory contains polynomial functions which are locally homeomorphic with a dense, denumerable metric space R* and are inherently quantized. Eigenfunctions governing fields can then be effectively obtained by computational iteration. Postulating a Lagrangian for fields in a compactified space-time, we get a general description of which the Schrodinger equation is a special case. From these results we can then also show that this denumerable space-time is relational (in the sense that space is not infinitesimally small if and only if it contains a quantized field) and, since Q2 is imbedded in R*2, it directly fulfills the strict topological requirements for Einstein-Weyl causality. Therefore, the theory predicts that E = R*.

  19. Ruling Out Multi-Order Interference in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Sinha, Urbasi; Couteau, Christophe; Jennewein, Thomas; Laflamme, Raymond; Weihs, Gregor

    2010-07-01

    Quantum mechanics and gravitation are two pillars of modern physics. Despite their success in describing the physical world around us, they seem to be incompatible theories. There are suggestions that one of these theories must be generalized to achieve unification. For example, Born’s rule—one of the axioms of quantum mechanics—could be violated. Born’s rule predicts that quantum interference, as shown by a double-slit diffraction experiment, occurs from pairs of paths. A generalized version of quantum mechanics might allow multipath (i.e., higher-order) interference, thus leading to a deviation from the theory. We performed a three-slit experiment with photons and bounded the magnitude of three-path interference to less than 10-2 of the expected two-path interference, thus ruling out third- and higher-order interference and providing a bound on the accuracy of Born’s rule. Our experiment is consistent with the postulate both in semiclassical and quantum regimes.

  20. PREFACE: EmQM13: Emergent Quantum Mechanics 2013

    NASA Astrophysics Data System (ADS)

    2014-04-01

    These proceedings comprise the invited lectures of the second international symposium on Emergent Quantum Mechanics (EmQM13), which was held at the premises of the Austrian Academy of Sciences in Vienna, Austria, 3-6 October 2013. The symposium was held at the ''Theatersaal'' of the Academy of Sciences, and was devoted to the open exploration of emergent quantum mechanics, a possible ''deeper level theory'' that interconnects three fields of knowledge: emergence, the quantum, and information. Could there appear a revised image of physical reality from recognizing new links between emergence, the quantum, and information? Could a novel synthesis pave the way towards a 21st century, ''superclassical'' physics? The symposium provided a forum for discussing (i) important obstacles which need to be overcome as well as (ii) promising developments and research opportunities on the way towards emergent quantum mechanics. Contributions were invited that presented current advances in both standard as well as unconventional approaches to quantum mechanics. The EmQM13 symposium was co-organized by Gerhard Grössing (Austrian Institute for Nonlinear Studies (AINS), Vienna), and by Jan Walleczek (Fetzer Franklin Fund, USA, and Phenoscience Laboratories, Berlin). After a very successful first conference on the same topic in 2011, the new partnership between AINS and the Fetzer Franklin Fund in producing the EmQM13 symposium was able to further expand interest in the promise of emergent quantum mechanics. The symposium consisted of two parts, an opening evening addressing the general public, and the scientific program of the conference proper. The opening evening took place at the Great Ceremonial Hall (Grosser Festsaal) of the Austrian Academy of Sciences, and it presented talks and a panel discussion on ''The Future of Quantum Mechanics'' with three distinguished speakers: Stephen Adler (Princeton), Gerard 't Hooft (Utrecht) and Masanao Ozawa (Nagoya). The articles contained in

  1. On the consistent histories approach to quantum mechanics

    SciTech Connect

    Dowker, F. |; Kent, A.

    1996-03-01

    We review the consistent histories formulations of quantum mechanics developed by Griffiths, Omnes, Gell-Man, and Hartle, and we describe the classifications of consistent sets. We illustrate some general features of consistent sets by a few lemmas and examples. We also consider various interpretations of the formalism, and we examine the new problems which arise in reconstructing the past and predicting the future. It is shown that Omnes characterization of true statements---statements that can be deduced unconditionally in his interpretation---is incorrect. We examine critically Gell-Mann and Hartle`s interpretation of the formalism, and in particular, their discussions of communication, prediction, and retrodiction, and we conclude that their explanation of the apparent persistence of quasiclassicality relies on assumptions about an as-yet-unknown theory of experience. Our overall conclusion is that the consistent histories approach illustrates the need to supplement quantum mechanics by some selection principle in order to produce a fundamental theory capable of unconditional predictions.

  2. Single particle wavefunction localizations in bulged CdSenanowires

    SciTech Connect

    Zhao, Zhengji; Wang, Lin-Wang; Wu, Fengmin

    2006-07-02

    Using atomistic empirical pseudopotentials, we havecalculated the electronic structures of CdSe nanowires with a bulgedarea. The localized state wavefunctions and their binding energies arecalculated, and their dependences on the bulged area shape are analyzed.We find that both the binding energy and the wavefunction localizationstrongly depend on the bulged area shape, with the most compact shapeproduces the largest binding energy and strongest wavefunctionlocalization. We also find that the top of the valence band state has aweaker localization than the bottom of the conduction band state due toan effective mass anisotropy.

  3. PREFACE: Singular interactions in quantum mechanics: solvable models

    NASA Astrophysics Data System (ADS)

    Dell'Antonio, Gianfausto; Exner, Pavel; Geyler, Vladimir

    2005-06-01

    conditions at vertices directly. Two papers are devoted to inverse problems in this context: M Harmer studies inverse scattering for the matrix Schrödinger operator on the halfline with applications to star graphs, while P Kurasov and M Nowaczyk give a mathematically rigorous version of the known Gutkin-Smilansky result on the inverse spectral problem. The paper by O Post contributes to the question of how graphs can be approximated by more realistic `fat' graphs, and describes a class leading to disconnected quantum graphs. Finally, S Kondej and one of the editors study scattering in the context of `leaky' graphs which takes quantum tunnelling into account. While most results in this field describe one-particle Hamiltonians, more complicated systems have also been studied. In this issue we have three examples. C Cacciapuito, R Carlone, and R Figari discuss decoherence in a simple model of two particles, one heavy and one light, interacting through a δ potential; they give a rigorous meaning to a formula derived by Joos and Zeh. A related model by R Figari and A Teta is used to describe ionization. M Hallnäs, E Langmann, and C Paufler treat a true N-body situation, namely a model of one-dimensional gas of distinguishable particles interacting through generalized point interactions; they write the Bethe ansatz and present the solution of a particular case. The last group is a collection of contributions which in one sense or another are outside quantum mechanics, either modifying its postulates or applying it to a different physical situation. The latter applies to the paper of D Noja and A Posilicano in which they study nonlinear wave equations with point perturbations and show the existence of a solution to the Cauchy problem. F Coutinho et al discuss one-dimensional point interactions with energy-dependent coupling constant, S Albeverio and S Kuzhel examine a class of point interactions which are not symmetric but P-symmetric, where P is the parity operator, and M

  4. Perturbatively deformed defects in Pöschl-Teller-driven scenarios for quantum mechanics

    NASA Astrophysics Data System (ADS)

    Bernardini, Alex E.; da Rocha, Roldão

    2016-07-01

    Pöschl-Teller-driven solutions for quantum mechanical fluctuations are triggered off by single scalar field theories obtained through a systematic perturbative procedure for generating deformed defects. The analytical properties concerning the quantum fluctuations in one-dimension, zero-mode states, first- and second-excited states, and energy density profiles are all obtained from deformed topological and non-topological structures supported by real scalar fields. Results are firstly derived from an integrated λϕ4 theory, with corresponding generalizations applied to starting λχ4 and sine-Gordon theories. By focusing our calculations on structures supported by the λϕ4 theory, the outcome of our study suggests an exact quantitative correspondence to Pöschl-Teller-driven systems. Embedded into the perturbative quantum mechanics framework, such a correspondence turns into a helpful tool for computing excited states and continuous mode solutions, as well as their associated energy spectrum, for quantum fluctuations of perturbatively deformed structures. Perturbative deformations create distinct physical scenarios in the context of exactly solvable quantum systems and may also work as an analytical support for describing novel braneworld universes embedded into a 5-dimensional gravity bulk.

  5. Student ability to distinguish between superposition states and mixed states in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Passante, Gina; Emigh, Paul J.; Shaffer, Peter S.

    2015-12-01

    Superposition gives rise to the probabilistic nature of quantum mechanics and is therefore one of the concepts at the heart of quantum mechanics. Although we have found that many students can successfully use the idea of superposition to calculate the probabilities of different measurement outcomes, they are often unable to identify the experimental implications of a superposition state. In particular, they fail to recognize how a superposition state and a mixed state (sometimes called a "lack of knowledge" state) can produce different experimental results. We present data that suggest that superposition in quantum mechanics is a difficult concept for students enrolled in sophomore-, junior-, and graduate-level quantum mechanics courses. We illustrate how an interactive lecture tutorial can improve student understanding of quantum mechanical superposition. A longitudinal study suggests that the impact persists after an additional quarter of quantum mechanics instruction that does not specifically address these ideas.

  6. The measurement problem in quantum mechanics: A phenomenological investigation

    NASA Astrophysics Data System (ADS)

    Hunter, Joel Brooks

    2008-10-01

    This dissertation is a phenomenological investigation of the measurement problem in quantum mechanics. The primary subject matter for description and analysis is scientific instruments and their use in experiments which elicit the measurement problem. A methodological critique is mounted against the ontological commitments taken for granted in the canonical interpretations of quantum theory and the scientific activity of measurement as the necessary interface between theoretical interest and perceptual results. I argue that an aesthetic dimension of reality functions as aproto-scientific establishment of sense-making that constantly operates to set integratively all other cognitively neat determinations, including scientifically rendered objects that are intrinsically non-visualizable. The way in which data "key in" to the original and originative register of the sensible in observation is clarified by examining prostheses, measuring apparatuses and instruments that are sense-conveying and -integrative with the human sensorium. Experiments, technology and instrumentation are examined in order to understand how knowing and that which is known is bonded by praxis-aisthesis. Quantum measurement is a praxic-dynamie activity and homologically structured and structur ing functional engagement in terms of instantiation, quantifiability, and spatiotemporal differentiation. The distinctions between a beauty-aesthetic and praxis-aisthesis are delineated. It is argued that a beauty-aesthetic is a construal of the economic dimension of scientific objects and work, and is not the primary manner in which the aesthetic dimension is disclosed. The economic dimension of abstractions reduces to an austere aesthetic of calculative economy. Nature itself, however, is not stingy; it is intrinsically capacious, extravagant, full of surprise, nuance, ambiguity and allusiveness. The capaciousness of Nature and the way in which we are integratively set within Nature in a materiality

  7. On the quantum mechanics of consciousness, with application to anomalous phenomena

    SciTech Connect

    Jahn, R.G.; Dunne, B.J.

    1986-08-01

    Theoretical explication of a growing body of empirical data on consciousness-related anomalous phenomena is unlikely to be achieved in terms of known physical processes. Rather, it will first be necessary to formulate the basic role of consciousness in the definition of reality before such anomalous experience can adequately be represented. This paper takes the position that reality is constituted only in the interaction of consciousness with its environment, and therefore that any scheme of conceptual organization developed to represent that reality must reflect the processes of consciousness as well as those of its environment. In this spirit, the concepts and formalisms of elementary quantum mechanics, as originally proposed to explain anomalous atomic-scale physical phenomena, are appropriated via metaphor to represent the general characteristics of consciousness interacting with any environment. More specifically, if consciousness is represented by a quantum mechanical wave function, and its environment by an appropriate potential profile, Schrodinger wave mechanics defines eigenfunctions and eigenvalues that can be associated with the cognitive and emotional experiences of that consciousness in that environment. To articulate this metaphor it is necessary to associate certain aspects of the formalism, such as the coordinate system, the quantum numbers, and even the metric itself, with various impressionistic descriptors of consciousness, such as its intensity, perspective, approach/avoidance attitude, balance between cognitive and emotional activity, and receptive/assertive disposition.

  8. Novel symmetries in an interacting 𝒩 = 2 supersymmetric quantum mechanical model

    NASA Astrophysics Data System (ADS)

    Krishna, S.; Shukla, D.; Malik, R. P.

    2016-07-01

    In this paper, we demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting 𝒩 = 2 supersymmetric quantum mechanical model of a system of an electron moving on a sphere in the background of a magnetic monopole and establish its interpretation in the language of differential geometry. These discrete symmetries are, over and above, the usual three continuous symmetries of the theory which together provide the physical realizations of the de Rham cohomological operators of differential geometry. We derive the nilpotent 𝒩 = 2 SUSY transformations by exploiting our idea of supervariable approach and provide geometrical meaning to these transformations in the language of Grassmannian translational generators on a (1, 2)-dimensional supermanifold on which our 𝒩 = 2 SUSY quantum mechanical model is generalized. We express the conserved supercharges and the invariance of the Lagrangian in terms of the supervariables (obtained after the imposition of the SUSY invariant restrictions) and provide the geometrical meaning to (i) the nilpotency property of the 𝒩 = 2 supercharges, and (ii) the SUSY invariance of the Lagrangian of our 𝒩 = 2 SUSY theory.

  9. On the Notion of Truth in Quantum Mechanics: a Category-Theoretic Standpoint

    NASA Astrophysics Data System (ADS)

    Karakostas, Vassilios; Zafiris, Elias

    The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valuation in quantum mechanics as exemplified, in particular, by Kochen-Specker's theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event algebras. We show explicitly that the latter category is equipped with an object of truth values, or classifying object, which constitutes the appropriate tool for assigning truth values to propositions describing the behavior of quantum systems. Effectively, this category-theoretic representation scheme circumvents consistently the semantic ambiguity with respect to truth valuation that is inherent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical implications of the resulting account are analyzed. We argue that it subscribes neither to a pragmatic instrumental nor to a relative notion of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature. In this light, the transcendence condition of the usual conception of correspondence truth is superseded by a reflective-like transcendental reasoning of the proposed account of truth that is suitable to the quantum domain of discourse.

  10. Recent Progress in Treating Protein–Ligand Interactions with Quantum-Mechanical Methods

    PubMed Central

    Yilmazer, Nusret Duygu; Korth, Martin

    2016-01-01

    We review the first successes and failures of a “new wave” of quantum chemistry-based approaches to the treatment of protein/ligand interactions. These approaches share the use of “enhanced”, dispersion (D), and/or hydrogen-bond (H) corrected density functional theory (DFT) or semi-empirical quantum mechanical (SQM) methods, in combination with ensemble weighting techniques of some form to capture entropic effects. Benchmark and model system calculations in comparison to high-level theoretical as well as experimental references have shown that both DFT-D (dispersion-corrected density functional theory) and SQM-DH (dispersion and hydrogen bond-corrected semi-empirical quantum mechanical) perform much more accurately than older DFT and SQM approaches and also standard docking methods. In addition, DFT-D might soon become and SQM-DH already is fast enough to compute a large number of binding modes of comparably large protein/ligand complexes, thus allowing for a more accurate assessment of entropic effects. PMID:27196893

  11. Recent Progress in Treating Protein-Ligand Interactions with Quantum-Mechanical Methods.

    PubMed

    Yilmazer, Nusret Duygu; Korth, Martin

    2016-01-01

    We review the first successes and failures of a "new wave" of quantum chemistry-based approaches to the treatment of protein/ligand interactions. These approaches share the use of "enhanced", dispersion (D), and/or hydrogen-bond (H) corrected density functional theory (DFT) or semi-empirical quantum mechanical (SQM) methods, in combination with ensemble weighting techniques of some form to capture entropic effects. Benchmark and model system calculations in comparison to high-level theoretical as well as experimental references have shown that both DFT-D (dispersion-corrected density functional theory) and SQM-DH (dispersion and hydrogen bond-corrected semi-empirical quantum mechanical) perform much more accurately than older DFT and SQM approaches and also standard docking methods. In addition, DFT-D might soon become and SQM-DH already is fast enough to compute a large number of binding modes of comparably large protein/ligand complexes, thus allowing for a more accurate assessment of entropic effects. PMID:27196893

  12. Novel symmetries in an interacting 𝒩 = 2 supersymmetric quantum mechanical model

    NASA Astrophysics Data System (ADS)

    Krishna, S.; Shukla, D.; Malik, R. P.

    2016-07-01

    In this paper, we demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting 𝒩 = 2 supersymmetric quantum mechanical model of a system of an electron moving on a sphere in the background of a magnetic monopole and establish its interpretation in the language of differential geometry. These discrete symmetries are, over and above, the usual three continuous symmetries of the theory which together provide the physical realizations of the de Rham cohomological operators of differential geometry. We derive the nilpotent 𝒩 = 2 SUSY transformations by exploiting our idea of supervariable approach and provide geometrical meaning to these transformations in the language of Grassmannian translational generators on a (1, 2)-dimensional supermanifold on which our 𝒩 = 2 SUSY quantum mechanical model is generalized. We express the conserved supercharges and the invariance of the Lagrangian in terms of the supervariables (obtained after the imposition of the SUSY invariant restrictions) and provide the geometrical meaning to (i) the nilpotency property of the 𝒩 = 2 supercharges, and (ii) the SUSY invariance of the Lagrangian of our 𝒩 = 2 SUSY theory.

  13. Dynamics of student modeling: A theory, algorithms, and application to quantum mechanics

    NASA Astrophysics Data System (ADS)

    Bao, Lei

    A good understanding of how students understand physics is of great importance for developing and delivering effective instructions. This research is an attempt to develop a coherent theoretical and mathematical framework to mode the student learning of physics. The theoretical foundation is based on useful ideas from theories in cognitive science, education, and physics education. The emphasis of this research is made on the development of a mathematical representation to model the important mental elements and the dynamics of these elements, and on numerical algorithms that allow quantitative evaluations of conceptual learning in physics. In part I, a model-based theoretical framework is proposed. Based on the theory, a mathematical representation and a set of data analysis algorithms are developed. This new method is called Model Analysis, which can be used to obtain quantitative evaluations on student models with data from multiple-choice questions. Two specific algorithms are discussed with great detail. The first algorithm is the concentration factor. It measures how student responses on multiple-choice questions are distributed. A significant concentration on certain choices of the questions often implies common student models corresponding to those choices. The second algorithm analyzes student responses to form student model vectors and student model density matrix. By decomposing the density matrix, we can obtain quantitative evaluations of specific models used by students. Application examples with data from FCI, FMCE, and Wave Test are discussed along with special treatments of the data to deal with the unique features of the different tests. Implications on test design techniques are also discussed with the results from the examples. Based on the theory and algorithms developed in part I, research is conducted to investigate student understandings of quantum mechanics. Common student models on classical prerequisites and important quantum concepts are

  14. Energy spectrum and wavefunction of electrons in hybrid superconducting nanowires

    NASA Astrophysics Data System (ADS)

    Kruchinin, S. P.

    2016-03-01

    Recent experiments have fabricated structured arrays. We study hybrid nanowires, in which normal and superconducting regions are in close proximity, by using the Bogoliubov-de Gennes equations for superconductivity in a cylindrical nanowire. We succeed to obtain the quantum energy levels and wavefunctions of a superconducting nanowire. The obtained spectra of electrons remind Hofstadter’s butterfly.

  15. Solitons in Skyrme - Faddeev spinor model and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Rybakov, Y.

    2016-07-01

    We discuss the possibility of unification of Skyrme and Faddeev approaches for the description of baryons and leptons respectively as topological solitons within the scope of 16-spinor model. The motivation for such a unification is based on a special 8- semispinor identity invented by the Italian geometrician F. Brioschi. This remarkable identity permits one to realize baryon or lepton states through the effect of spontaneous symmetry breaking emerging due to special structure of the Higgs potential in the model. At large distances from the particle - soliton small excitation of the vacuum satisfies Klein - Gordon equation with some mass that permits one to establish the correspondence with quantum mechanics in special stochastic representation of the wave function for extended particles - solitons. Finally, we illustrate the peculiar properties of stochastic representation by the famous T. Young's experiment with n slits in soliton realization.

  16. A Case Study of Teaching Quantum Mechanics Using Research Publications

    NASA Astrophysics Data System (ADS)

    Sharma, Manjula

    2015-04-01

    Significant research effort is dedicated to student learning of quantum mechanics. Students often find quantum interesting but are challenged by the abstraction. The mathematical detail detracts from the conceptual underpinnings. This presentation provides examples of innovating teaching which attempt to address these matters. It draws on an Australian Government Office for Learning and Teaching National Teaching Fellowship which involved 9 universities. The innovations use research publications in different ways within a lecture course. In some, papers which shaped the field are used to examine conceptual underpinnings, in some students critique research papers, and in others students search for papers to share with peers. The role of different face-to-face pedagogies such as whole class discussions and small group work will be discussed. Ways in which assessment has been changed will also be discussed.

  17. Quantum mechanism of nonlocal Gilbert damping in magnetic trilayers

    NASA Astrophysics Data System (ADS)

    Barati, Ehsan; Cinal, Marek

    2015-06-01

    A fully quantum-mechanical calculation of the Gilbert damping constant α in magnetic trilayers is done by employing the torque-correlation formula within a realistic tight-binding model. A remarkable enhancement of α in Co/NM1/NM2 trilayers is obtained due to adding the caps NM2=Pd, Pt, and it decays with the thickness of the spacers NM1=Cu, Ag, Au in agreement with experiment. Nonlocal origin of the Gilbert damping is visualized with its atomic layer contributions. It is shown that magnetization in Co is damped remotely by strong spin-orbit coupling in NM2 via quantum states with large amplitude in both Co and NM2.

  18. Vibrational spectra and quantum mechanical calculations of antiretroviral drugs: Nevirapine

    NASA Astrophysics Data System (ADS)

    Ayala, A. P.; Siesler, H. W.; Wardell, S. M. S. V.; Boechat, N.; Dabbene, V.; Cuffini, S. L.

    2007-02-01

    Nevirapine (11-cyclopropyl-5,11-dihydro-4-methyl-6H-dipyrido[3,2-b:2',3'e][1,4]diazepin-6-one) is an antiretroviral drug belonging to the class of the non-nucleoside inhibitors of the HIV-1 virus reverse transcriptase. As most of this kind of antiretroviral drugs, nevirapine displays a butterfly-like conformation which is preserved in complexes with the HIV-1 reverse transcriptase. In this work, we present a detailed vibrational spectroscopy investigation of nevirapine by using mid-infrared, near-infrared, and Raman spectroscopies. These data are supported by quantum mechanical calculations, which allow us to characterize completely the vibrational spectra of this compound. Based on these results, we discuss the correlation between the vibrational modes and the crystalline structure of the most stable form of nevirapine.

  19. Transforming Upper-Division Quantum Mechanics: Learning Goals and Assessment

    NASA Astrophysics Data System (ADS)

    Goldhaber, Steve; Pollock, Steven; Dubson, Mike; Beale, Paul; Perkins, Katherine

    2009-11-01

    In order to help students overcome documented difficulties learning quantum mechanics (QM) concepts, we have transformed our upper-division QM I course using principles of learning theory and active engagement. Key components of this process include establishing learning goals and developing a valid, reliable conceptual assessment tool to measure the extent to which students achieve these learning goals. The course learning goals were developed with broad faculty input, and serve as the basis for the design of the course assessment tool. The development of the assessment tool has included significant faculty input and feedback, twenty-one student interviews, a review of PER literature, and administration of the survey to two semesters of QM I students as well as to a cohort of graduate students. Here, we discuss this ongoing development process and present initial findings from our QM class for the past two semesters.

  20. Conformational analysis of small molecules: NMR and quantum mechanics calculations.

    PubMed

    Tormena, Cláudio F

    2016-08-01

    This review deals with conformational analysis in small organic molecules, and describes the stereoelectronic interactions responsible for conformational stability. Conformational analysis is usually performed using NMR spectroscopy through measurement of coupling constants at room or low temperature in different solvents to determine the populations of conformers in solution. Quantum mechanical calculations are used to address the interactions responsible for conformer stability. The conformational analysis of a large number of small molecules is described, using coupling constant measurements in different solvents and at low temperature, as well as recent applications of through-space and through-hydrogen bond coupling constants JFH as tools for the conformational analysis of fluorinated molecules. Besides NMR parameters, stereoelectronic interactions such as conjugative, hyperconjugative, steric and intramolecular hydrogen bond interactions involved in conformational preferences are discussed.

  1. Reflections on Zeilinger-Brukner Information Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei

    2016-07-01

    In this short review I present my personal reflections on Zeilinger-Brukner information interpretation of quantum mechanics (QM).In general, this interpretation is very attractive for me. However, its rigid coupling to the notion of irreducible quantum randomness is a very complicated issue which I plan to address in more detail. This note may be useful for general public interested in quantum foundations, especially because I try to analyze essentials of the information interpretation critically (i.e., not just emphasizing its advantages as it is commonly done). This review is written in non-physicist friendly manner. Experts actively exploring this interpretation may be interested in the paper as well, as in the comments of "an external observer" who have been monitoring the development of this approach to QM during the last 18 years. The last part of this review is devoted to the general methodology of science with references to views of de Finetti, Wigner, and Peres.

  2. Quantum Probability Theory and the Foundations of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Fröhlich, Jürg; Schubnel, Baptiste

    By and large, people are better at coining expressions than at filling them with interesting, concrete contents. Thus, it may not be very surprising that there are many professional probabilists who may have heard the expression but do not appear to be aware of the need to develop "quantum probability theory" into a thriving, rich, useful field featured at meetings and conferences on probability theory. Although our aim, in this essay, is not to contribute new results on quantum probability theory, we hope to be able to let the reader feel the enormous potential and richness of this field. What we intend to do, in the following, is to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras).

  3. Classical and quantum mechanics of the nonrelativistic Snyder model

    NASA Astrophysics Data System (ADS)

    Mignemi, S.

    2011-07-01

    The Snyder model is an example of noncommutative spacetime admitting a fundamental length scale β and invariant under Lorentz transformations, that can be interpreted as a realization of the doubly special relativity axioms. Here, we consider its nonrelativistic counterpart, i.e. the Snyder model restricted to three-dimensional Euclidean space. We discuss the classical and the quantum mechanics of a free particle in this framework, and show that they strongly depend on the sign of a coupling constant λ, appearing in the fundamental commutators and proportional to β2. For example, if λ is negative, momenta are bounded. On the contrary, for positive λ, positions and areas are quantized. We also give the exact solution of the harmonic oscillator equations both in the classical and the quantum case, and show that its frequency is energy dependent.

  4. Gauge transformations and conserved quantities in classical and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Berche, Bertrand; Malterre, Daniel; Medina, Ernesto

    2016-08-01

    We are taught that gauge transformations in classical and quantum mechanics do not change the physics of the problem. Nevertheless, here we discuss three broad scenarios where under gauge transformations: (i) conservation laws are not preserved in the usual manner; (ii) non-gauge-invariant quantities can be associated with physical observables; and (iii) there are changes in the physical boundary conditions of the wave function that render it non-single-valued. We give worked examples that illustrate these points, in contrast to general opinions from classic texts. We also give a historical perspective on the development of Abelian gauge theory in relation to our particular points. Our aim is to provide a discussion of these issues at the graduate level.

  5. Quantum Mechanical Free Energy Barrier for an Enzymatic Reaction

    NASA Astrophysics Data System (ADS)

    Rod, Thomas H.; Ryde, Ulf

    2005-04-01

    We discuss problems related to in silico studies of enzymes and show that accurate and converged free energy changes for complex chemical reactions can be computed if a method based on a thermodynamic cycle is employed. The method combines the sampling speed of molecular mechanics with the accuracy of a high-level quantum mechanics method. We use the method to compute the free energy barrier for a methyl transfer reaction catalyzed by the enzyme catechol O-methyltransferase at the level of density functional theory. The surrounding protein and solvent are found to have a profound effect on the reaction, and we show that energies can be extrapolated easily from one basis set and exchange-correlation functional to another. Using this procedure we calculate a barrier of 69 kJ/mol, in excellent agreement with the experimental value of 75 kJ/mol.

  6. Perspective: Quantum mechanical methods in biochemistry and biophysics

    NASA Astrophysics Data System (ADS)

    Cui, Qiang

    2016-10-01

    In this perspective article, I discuss several research topics relevant to quantum mechanical (QM) methods in biophysical and biochemical applications. Due to the immense complexity of biological problems, the key is to develop methods that are able to strike the proper balance of computational efficiency and accuracy for the problem of interest. Therefore, in addition to the development of novel ab initio and density functional theory based QM methods for the study of reactive events that involve complex motifs such as transition metal clusters in metalloenzymes, it is equally important to develop inexpensive QM methods and advanced classical or quantal force fields to describe different physicochemical properties of biomolecules and their behaviors in complex environments. Maintaining a solid connection of these more approximate methods with rigorous QM methods is essential to their transferability and robustness. Comparison to diverse experimental observables helps validate computational models and mechanistic hypotheses as well as driving further development of computational methodologies.

  7. Maximum-power quantum-mechanical Carnot engine.

    PubMed

    Abe, Sumiyoshi

    2011-04-01

    In their work [J. Phys. A 33, 4427 (2000)], Bender, Brody, and Meister have shown by employing a two-state model of a particle confined in the one-dimensional infinite potential well that it is possible to construct a quantum-mechanical analog of the Carnot engine through changes of both the width of the well and the quantum state in a specific manner. Here, a discussion is developed about realizing the maximum power of such an engine, where the width of the well moves at low but finite speed. The efficiency of the engine at the maximum power output is found to be universal independently of any of the parameters contained in the model.

  8. Neutrino oscillations: Quantum mechanics vs. quantum field theory

    SciTech Connect

    Akhmedov, Evgeny Kh.; Kopp, Joachim

    2010-01-01

    A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.

  9. Conformational analysis of small molecules: NMR and quantum mechanics calculations.

    PubMed

    Tormena, Cláudio F

    2016-08-01

    This review deals with conformational analysis in small organic molecules, and describes the stereoelectronic interactions responsible for conformational stability. Conformational analysis is usually performed using NMR spectroscopy through measurement of coupling constants at room or low temperature in different solvents to determine the populations of conformers in solution. Quantum mechanical calculations are used to address the interactions responsible for conformer stability. The conformational analysis of a large number of small molecules is described, using coupling constant measurements in different solvents and at low temperature, as well as recent applications of through-space and through-hydrogen bond coupling constants JFH as tools for the conformational analysis of fluorinated molecules. Besides NMR parameters, stereoelectronic interactions such as conjugative, hyperconjugative, steric and intramolecular hydrogen bond interactions involved in conformational preferences are discussed. PMID:27573182

  10. Perspective: Quantum mechanical methods in biochemistry and biophysics

    PubMed Central

    Cui, Qiang

    2016-01-01

    In this perspective article, I discuss several research topics relevant to quantum mechanical (QM) methods in biophysical and biochemical applications. Due to the immense complexity of biological problems, the key is to develop methods that are able to strike the proper balance of computational efficiency and accuracy for the problem of interest. Therefore, in addition to the development of novel ab initio and density functional theory based QM methods for the study of reactive events that involve complex motifs such as transition metal clusters in metalloenzymes, it is equally important to develop inexpensive QM methods and advanced classical or quantal force fields to describe different physicochemical properties of biomolecules and their behaviors in complex environments. Maintaining a solid connection of these more approximate methods with rigorous QM methods is essential to their transferability and robustness. Comparison to diverse experimental observables helps validate computational models and mechanistic hypotheses as well as driving further development of computational methodologies. PMID:27782516

  11. Teaching Quantum Mechanics through Project-based Learning

    NASA Astrophysics Data System (ADS)

    Duda, Gintaras; Ward, Kristina

    2014-03-01

    Project/Problem-based learning (PBL) is an active area of research within the physics education research (PER) community, however, work done to date has focused on introductory courses. This talk will explore research on upper division quantum mechanics, a junior/senior level course at Creighton University, which was taught using PBL pedagogy with no in-class lectures. Course time was primarily spent on lecture tutorials and projects, which included alpha decay of Uranium, neutrino oscillations, and FTIR spectroscopy of HCl. This talk will explore: 1. student learning in light of the new pedagogy and embedded meta-cognitive self-monitoring exercises, 2. the effect of the PBL curriculum on student attitudes, motivation, and students' epistemologies, and 3. the use of explicit written reflections within a physics course to probe student understanding.

  12. Is Quantum Mechanics Incompatible with Newton's First Law?

    NASA Astrophysics Data System (ADS)

    Rabinowitz, Mario

    2008-04-01

    Quantum mechanics (QM) clearly violates Newton’s First Law of Motion (NFLM) in the quantum domain for one of the simplest problems, yielding an effect in a force-free region much like the Aharonov-Bohm effect. In addition, there is an incompatibility between the predictions of QM in the classical limit, and that of classical mechanics (CM) with respect to NFLM. A general argument is made that such a disparity may be found commonly for a wide variety of quantum predictions in the classical limit. Alternatives to the Schrödinger equation are considered that might avoid this problem. The meaning of the classical limit is examined. Critical views regarding QM by Schrödinger, Bohm, Bell, Clauser, and others are presented to provide a more complete perspective.

  13. Black hole thermodynamics from near-horizon conformal quantum mechanics

    SciTech Connect

    Camblong, Horacio E.; Ordonez, Carlos R.

    2005-05-15

    The thermodynamics of black holes is shown to be directly induced by their near-horizon conformal invariance. This behavior is exhibited using a scalar field as a probe of the black hole gravitational background, for a general class of metrics in D spacetime dimensions (with D{>=}4). The ensuing analysis is based on conformal quantum mechanics, within a hierarchical near-horizon expansion. In particular, the leading conformal behavior provides the correct quantum statistical properties for the Bekenstein-Hawking entropy, with the near-horizon physics governing the thermodynamics from the outset. Most importantly: (i) this treatment reveals the emergence of holographic properties; (ii) the conformal coupling parameter is shown to be related to the Hawking temperature; and (iii) Schwarzschild-like coordinates, despite their 'coordinate singularity', can be used self-consistently to describe the thermodynamics of black holes.

  14. Quantum mechanics calculation of catalytic properties of a copper sensor for prediction of flow characteristics in plasmatron

    NASA Astrophysics Data System (ADS)

    Kovalev, V. L.; Kroupnov, A. A.; Vetchinkin, А. S.

    2015-12-01

    Basing on quantum-mechanical calculations within cluster models, rate coefficients of elementary steps of the complete system of heterogeneous catalytic recombination of dissociated oxygen on the copper oxide surface were determined. They were used for calculation of dependence of the effective coefficient of oxygen atom heterogeneous catalytic recombination on the temperature and partial pressure in a wide range of conditions at the surface. It has been established that its value substantially varies depending on the conditions at the surface.

  15. The Kantian element in the Copenhagen interpretation of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Cale, David Lee

    In Quantum Physics and the Philosophical Tradition, Aage Petersen makes the troubling claim that the entirety of the tradition of Western philosophy is "deconstructed" by quantum mechanics. This viewpoint applies, especially, to the relationship between Kantian philosophy and quantum theory. It is generally accepted that quantum mechanics, in its Copenhagen interpretation, has destroyed all validity for the classical belief in a deterministic underlying reality, a belief sustained throughout the nineteenth century through a philosophical ground in Kant's critical philosophy. This dissertation takes on the daunting task of determining what, if any, relationship can be had between contemporary physics and Kantian philosophy. It begins with a historical review of the challenges posed for Kant's arguments and proposed solutions, especially those offered by Cassirer. It then turns to the task of providing the Western philosophical tradition with an interpretation apart from Petersen's, which sees it as concerned only with the problem of being. The offered solution is the suggestion that Western philosophy be understood as a struggle, between epistemological and ontological perspectives, to provide a context for the various descriptions of nature provided by human scientific progress. Kant's philosophy is then interpreted as an effort to provide Newtonian physics with a valid context in the face of Hume's skepticism. The finding is that Kant was the first to suggest that an object does not acquire the spatio-temporal properties used in its physical description until introduced to an observer. The dissertation concludes that the authors of the Copenhagen interpretation were essentially engaged in Kant's enterprise through their attempt to provide an observer based context for the spatio-temporal descriptive principles used in the physics of their time.

  16. Testing Quantum Mechanics and Bell's Inequality with Astronomical Observations

    NASA Astrophysics Data System (ADS)

    Friedman, Andrew S.; Kaiser, David I.; Gallicchio, Jason; Team 1: University of Vienna, InstituteQuantum Optics and Quantum Information; Team 2: UC San Diego Cosmology Group; Team 3: NASA/JPL/Caltech

    2016-06-01

    We report on an in progress "Cosmic Bell" experiment that will leverage cosmology to test quantum mechanics and Bell's inequality using astronomical observations. Different iterations of our experiment will send polarization-entangled photons through the open air to detectors ~1-100 kilometers apart, whose settings would be rapidly chosen using real-time telescopic observations of Milky Way stars, and eventually distant, causally disconnected, cosmological sources - such as pairs of quasars or patches of the cosmic microwave background - all while the entangled pair is still in flight. This would, for the first time, attempt to fully close the so-called "setting independence" or "free will" loophole in experimental tests of Bell's inequality, whereby an alternative theory could mimic the quantum predictions if the experimental settings choices shared even a small correlation with unknown, local, causal influences a mere few milliseconds prior to the experiment. A full Cosmic Bell test would push any such influence all the way back to the hot big bang, since the end of any period of inflation, 13.8 billion years ago, an improvement of 20 orders of magnitude compared to the best previous experiments. Redshift z > 3.65 quasars observed at optical wavelengths are the optimal candidate source pairs using present technology. Our experiment is partially funded by the NSF INSPIRE program, in collaboration with MIT, UC San Diego, Harvey Mudd College, NASA/JPL/Caltech, and the University of Vienna. Such an experiment has implications for our understanding of nature at the deepest level. By testing quantum mechanics in a regime never before explored, we would at the very least extend our confidence in quantum theory, while at the same time severely constraining large classes of alternative theories. If the experiment were to uncover discrepancies from the quantum predictions, there could be crucial implications for early-universe cosmology, the security of quantum encryption

  17. A novel quantum-mechanical interpretation of the Dirac equation

    NASA Astrophysics Data System (ADS)

    K-H Kiessling, M.; Tahvildar-Zadeh, A. S.

    2016-04-01

    A novel interpretation is given of Dirac’s ‘wave equation for the relativistic electron’ as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different ‘topological spin’ states of a single more fundamental particle, not distinct particles in their own right. The new interpretation is backed up by the existence of such ‘bi-particle’ structures in general relativity, in particular the ring singularity present in any spacelike section of the spacetime singularity of the maximal-analytically extended, topologically non-trivial, electromagnetic Kerr-Newman (KN)spacetime in the zero-gravity limit (here, ‘zero-gravity’ means the limit G\\to 0, where G is Newton’s constant of universal gravitation). This novel interpretation resolves the dilemma that Dirac’s wave equation seems to be capable of describing both the electron and the positron in ‘external’ fields in many relevant situations, while the bi-spinorial wave function has only a single position variable in its argument, not two—as it should if it were a quantum-mechanical two-particle wave equation. A Dirac equation is formulated for such a ring-like bi-particle which interacts with a static point charge located elsewhere in the topologically non-trivial physical space associated with the moving ring particle, the motion being governed by a de Broglie-Bohm type law extracted from the Dirac equation. As an application, the pertinent general-relativistic zero-gravity hydrogen problem is studied in the usual Born-Oppenheimer approximation. Its spectral results suggest that the zero-G KN magnetic moment be identified with the so-called ‘anomalous magnetic moment of the physical electron,’ not with the Bohr magneton, so that the ring radius is only a tiny fraction of the electron’s reduced Compton wavelength.

  18. Coulomb problem in non-commutative quantum mechanics

    SciTech Connect

    Galikova, Veronika; Presnajder, Peter

    2013-05-15

    The aim of this paper is to find out how it would be possible for space non-commutativity (NC) to alter the quantum mechanics (QM) solution of the Coulomb problem. The NC parameter {lambda} is to be regarded as a measure of the non-commutativity - setting {lambda}= 0 which means a return to the standard quantum mechanics. As the very first step a rotationally invariant NC space R{sub {lambda}}{sup 3}, an analog of the Coulomb problem configuration space (R{sup 3} with the origin excluded) is introduced. R{sub {lambda}}{sup 3} is generated by NC coordinates realized as operators acting in an auxiliary (Fock) space F. The properly weighted Hilbert-Schmidt operators in F form H{sub {lambda}}, a NC analog of the Hilbert space of the wave functions. We will refer to them as 'wave functions' also in the NC case. The definition of a NC analog of the hamiltonian as a hermitian operator in H{sub {lambda}} is one of the key parts of this paper. The resulting problem is exactly solvable. The full solution is provided, including formulas for the bound states for E < 0 and low-energy scattering for E > 0 (both containing NC corrections analytic in {lambda}) and also formulas for high-energy scattering and unexpected bound states at ultra-high energy (both containing NC corrections singular in {lambda}). All the NC contributions to the known QM solutions either vanish or disappear in the limit {lambda}{yields} 0.

  19. Mixed ab initio quantum mechanics/molecular mechanics methods using frozen orbitals with applications to peptides and proteins

    NASA Astrophysics Data System (ADS)

    Philipp, Dean Michael

    Methodology is discussed for mixed ab initio quantum mechanics/molecular mechanics modeling of systems where the quantum mechanics (QM) and molecular mechanics (MM) regions are within the same molecule. The ab initio QM calculations are at the restricted Hartree-Fock level using the pseudospectral method of the Jaguar program while the MM part is treated with the OPLS force fields implemented in the IMPACT program. The interface between the QM and MM regions, in particular, is elaborated upon, as it is dealt with by ``breaking'' bonds at the boundaries and using Boys-localized orbitals found from model molecules in place of the bonds. These orbitals are kept frozen during QM calculations. The mixed modeling presented here can be used for single point energy calculations and geometry optimizations. Results from tests of the method to find relative conformational energies and geometries of alanine tetrapeptides are presented along with comparisons to pure QM and pure MM calculations.

  20. Josephson junction devices: Model quantum mechanical systems and medical applications

    NASA Astrophysics Data System (ADS)

    Chen, Josephine

    In this dissertation, three experiments using Josephson junction devices are described. In Part I, the effect of dissipation on tunneling between charge states in a superconducting single-electron transistor (sSET) was studied. The sSET was fabricated on top of a semi-conductor heterostructure with a two-dimensional electron gas (2DEG) imbedded beneath the surface. The 2DEG acted as a dissipative ground plane. The sheet resistance of the 2DEG could be varied in situ by applying a large voltage to a gate on the back of the substrate. The zero-bias conductance of the sSET was observed to increase with increasing temperature and 2DEG resistance. Some qualitative but not quantitative agreement was found with theoretical calculations of the functional dependence of the conductance on temperature and 2DEG resistance. Part II describes a series of experiments performed on magnesium diboride point-contact junctions. The pressure between the MgB2 tip and base pieces could be adjusted to form junctions with different characteristics. With light pressure applied between the two pieces, quasiparticle tunneling in superconductor-insulator-superconductor junctions was measured. From these data, a superconducting gap of approximately 2 meV and a critical temperature of 29 K were estimated. Increasing the pressure between the MgB2 pieces formed junctions with superconductor-normal metal-superconductor characteristics. We used these junctions to form MgB2 superconducting quantum interference devices (SQUIDS). Noise levels as low as 35 fT/Hz1/2 and 4 muphi 0/Hz1/2 at 1 kHz were measured. In Part III, we used a SQUID-based instrument to acquire magnetocardiograms (MCG), the magnetic field signal measured from the human heart. We measured 51 healthy volunteers and 11 cardiac patients both at rest and after treadmill exercise. We found age and sex related differences in the MCG of the healthy volunteers that suggest that these factors should be considered when evaluating the MCG for disease. We also defined a spatio-temporal MCG parameter, the repolarization stabilization interval, which successfully discriminated our patients from our healthy controls.