相关论文
1997
The Hidden-Measurement Formalism: Quantum Mechanics as a Consequence of Fluctuations on the Measurement

We expose a formalism, that we have called the’ hidden measurement formalism’, where the quantum structure is due to the presence of ‘fluctuations’ on the interaction between the system and the measurement apparatus. In this formalism the quantum mechanical probabilities are not ontological but arrise as a consequence of ‘lack of knowledge’ about this interaction. We study the quantum classical limit and the EPR problem in the light of this explanation.

2006
How to Derive the Hilbert‐Space Formulation of Quantum Mechanics From Purely Operational Axioms

In the present paper I show how it is possible to derive the Hilbert space formulation of Quantum Mechanics from a comprehensive definition of physical experiment and assuming experimental accessibility and simplicity as specified by five simple Postulates. This accomplishes the program presented in form of conjectures in the previous paper. Pivotal roles are played by the local observability principle, which reconciles the holism of nonlocality with the reductionism of local observation, and by the postulated existence of informationally complete observables and of a symmetric faithful state. This last notion allows one to introduce an operational definition for the real version of the “adjoint”—i. e. the transposition—from which one can derive a real Hilbert‐space structure via either the Mackey‐Kakutani or the Gelfand‐Naimark‐Segal constructions. Here I analyze in detail only the Gelfand‐Naimark‐Segal construction, which leads to a real Hilbert space structure analogous to that of (classes of generally...

2015 - Journal of chemical theory and computation
Hybrid Quantum Mechanics/Molecular Mechanics/Coarse Grained Modeling: A Triple-Resolution Approach for Biomolecular Systems.

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.

2011 - Journal of Biological Physics
Binding free energy calculation with QM/MM hybrid methods for Abl-Kinase inhibitor

We report a Quantum mechanics/Molecular Mechanics–Poisson-Boltzmann/ Surface Area (QM/MM-PB/SA) method to calculate the binding free energy of c-Abl human tyrosine kinase by combining the QM and MM principles where the ligand is treated quantum mechanically and the rest of the receptor by classical molecular mechanics. To study the role of entropy and the flexibility of the protein ligand complex in a solvated environment, molecular dynamics calculations are performed using a hybrid QM/MM approach. This work shows that the results of the QM/MM approach are strongly correlated with the binding affinity. The QM/MM interaction energy in our reported study confirms the importance of electronic and polarization contributions, which are often neglected in classical MM-PB/SA calculations. Moreover, a comparison of semi-empirical methods like DFTB-SCC, PM3, MNDO, MNDO-PDDG, and PDDG-PM3 is also performed. The results of the study show that the implementation of a DFTB-SCC semi-empirical Hamiltonian that is derived from DFT gives better results than other methods. We have performed such studies using the AMBER molecular dynamic package for the first time. The calculated binding free energy is also in agreement with the experimentally determined binding affinity for c-Abl tyrosine kinase complex with Imatinib.

2011 - Advanced Topics in Information Retrieval
Quantum Mechanics and Information Retrieval

In this chapter, we describe how the intersection between information retrieval and the quantum mechanical framework has been implemented. We select and present in no predefined order the most significant contributions to the implementation of this intersection; some contributions appear to be less mature than others; however, we decided to include them since they are sources of future work. Other contributions might appear less “quantum inspired” than others; however, each research work contains concepts and tools that are somehow linked to the quantum mechanical framework illustrated in the book. In the end, the contributions reported in this chapter cover a wide range of issues, from modeling issues to user interaction issues. The chapter ends with suggestions of further reading.

1995 - Synthese
Theories between theories: Asymptotic limiting intertheoretic relations

This paper addresses a relatively common “scientific” (as opposed to philosophical) conception of intertheoretic reduction between physical theories. This is the sense of reduction in which one (typically newer and more refined) theory is said to reduce to another (typically older and “coarser”) theory in the limit as some small parameter tends to zero. Three examples of such reductions are discussed: First, the reduction of Special Relativity (SR) to Newtonian Mechanics (NM) as (v/c)2→0; second, the reduction of wave optics to geometrical optics as λ → 0; and third, the reduction of Quantum Mechanics (QM) to Classical Mechanics (CM) asħ→0. I argue for the following two claims. First, the case of SR reducing to NM is an instance of a genuine reductive relationship while the latter two cases are not. The reason for this concerns the nature of the limiting relationships between the theory pairs. In the SR/NM case, it is possible to consider SR as a regular perturbation of NM; whereas in the cases of wave and geometrical optics and QM/CM, the perturbation problem is singular. The second claim I wish to support is that as a result of the singular nature of the limits between these theory pairs, it is reasonable to maintain that third theories exist describing the asymptotic limiting domains. In the optics case, such a theory has been called “catastrophe optics”. In the QM/CM case, it is semiclassical mechanics. Aspects of both theories are discussed in some detail.

2007 - Journal of Physics A
Derivation of the postulates of quantum mechanics from the first principles of scale relativity

Quantum mechanics is based on a series of postulates which lead to a very good description of the microphysical realm but which have, up to now, not been derived from first principles. In the present work, we suggest such a derivation in the framework of the theory of scale relativity. After having analyzed the actual status of the various postulates, rules and principles that underlie the present axiomatic foundation of quantum mechanics (in terms of main postulates, secondary rules and derived 'principles'), we attempt to provide the reader with an exhaustive view of the matter, by both gathering here results which are already available in the literature, and deriving new ones which complete the postulate list.

2010 - arXiv: Mathematical Physics
Principles of Fractional Quantum Mechanics

A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\'odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum mechanics, hermiticity of the Hamilton operator, parity conservation law and the current density. Applications of fractional quantum mechanics cover dynamics of a free particle, new representation for a free particle quantum mechanical kernel, infinite potential well, bound state in {\delta}-potential well, linear potential, fractional Bohr atom and fractional oscillator. We also review fundamentals of the L\'evy path integral approach to fractional statistical mechanics.

1973 - American Journal of Physics
Introduction to Field Operators in Quantum Mechanics

The equivalence of the field operator formulation of quantum mechanics and ordinary wave mechanics is proved in an efficient and elementary way. The discussion proceeds algebraically from the (anti-) commutation relations, which the field operators are defined to satisfy. Although the paper is introductory and presumes only a knowledge of elementary wave mechanics, it is intended to cover all of the essential elements of the subject in a rigorous way.

1951
The Quantum Mechanics of Assemblies of Interacting Particles

The quantum mechanics of fluids at moderately high and very low temperatures is investigated by the extension of a method due to Wigner. The fundamental equation satisfied by the phase space distribution function is solved, on the basis of classical statistics, by two different methods, and quantum corrections for thermodynamical equilibrium are obtained. It is shown that the effective molecular interaction becomes very weak near absolute zero. An estimate is made of the zero‐point energy. Corrections due to quantum statistics are obtained.

2002 - American Journal of Physics
Testing the development of student conceptual and visualization understanding in quantum mechanics through the undergraduate career

In order to probe various aspects of student understanding of some of the core ideas of quantum mechanics, and especially how they develop over the undergraduate curriculum, we have developed an assessment instrument designed to test conceptual and visualization understanding in quantum theory. We report data obtained from students ranging from sophomore-level modern physics courses, through junior–senior level quantum theory classes, to first year graduate quantum mechanics courses in what may be the first such study of the development of student understanding in this important core subject of physics through the undergraduate career. We discuss the results and their possible relevance to the standard curriculum as well as to the development of new curricular materials.

1961 - Journal of Chemical Physics
Quantum Mechanics of Mobile Electrons in Conjugated Bond Systems. III. Topological Matrix as Generatrix of Bond Orders

It is shown that in homonuclear conjugated systems the various bond orders and similar quantities can be written as matrix functions of the topological incidence matrix. This entails the existence of a number of useful general relations between these various quantities. The relations include as special cases: Coulson and Rushbrooke's theorem on charge orders in alternants; G. G. Hall's theorem on bond orders in alternants; McWeeny's theorem on the formal charges; Ham and Ruedenberg's correlation between Coulson and Mulliken bond orders for neighbors in alternants; closely related is Ham‐Ruedenberg‐Platt's relation between valence‐bond bond orders and molecular orbital theory. A number of new relations between bond orders are derived and discussed. The generalization from alternants to nonalternants is given particular attention.

1997 - Annals of Physics
NONPERTURBATIVE REGULARIZATION AND RENORMALIZATION : SIMPLE EXAMPLES FROM NONRELATIVISTIC QUANTUM MECHANICS

Abstract We examine several zero-range potentials in nonrelativistic quantum mechanics. The study of such potentials requires regularization and renormalization. We contrast physical results obtained using dimensional regularization and cutoff schemes and show explicitly that in certain cases dimensional regularization fails to reproduce the results obtained using cutoff regularization. First we consider a delta-function potential in arbitrary space dimensions. Using cutoff regularization we show that ford⩾4 the renormalized scattering amplitude is trivial. In contrast, dimensional regularization can yield a nontrivial scattering amplitude for odd dimensions greater than or equal to five. We also consider a potential consisting of a delta function plus the derivative-squared of a delta function in three dimensions. We show that the renormalized scattering amplitudes obtained using the two regularization schemes are different. Moreover, we find that in the cutoff-regulated calculation the effective range is necessarily negative in the limit that the cutoff is taken to infinity. In contrast, in dimensional regularization the effective range is unconstrained. We discuss how these discrepancies arise from the dimensional regularization prescription that all power-law divergences vanish. We argue that these results demonstrate that dimensional regularization can fail in a nonperturbative setting.

2015 - arXiv: Physics Education
A Review of Student Difficulties in Upper-Level Quantum Mechanics

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 multi-university 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 over-generalizations 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 approached that take advantage of research on student difficulties in order to improve teaching and learning of quantum mechanics.

1994 - Mind
A Neglected Route to Realism about Quantum Mechanics

Bell's Theorem assumes that hidden variables are not influenced by future measurement settings. The assumption has sometimes been questioned, but the suggestion has been thought outlandish, even by the taxed standards of the discipline. (Bell thought that it led to fatalism.) The case for this reaction turns out to be surprisingly weak, however. We show that QM easily evades the standard objections to advanced action. And the approach has striking advantages, especially in avoiding the apparent conflict between Bell's Theorem and special relativity. The second part of the paper considers the broader question as to why advanced action seems so counterintuitive. We investigate the origins of our ordinary intuitions about causal asymmetry. It is argued that the view that the past does not depend on the future is largely anthropocentric, a kind of projection of our own temporal asymmetry. Many physicists have also reached this conclusion, but have thought that if causation has no objective direction, there is no objective content to an advanced action interpretation of QM. This turns out to be a mistake. From the ordinary subjective perspective, we can distinguish two sorts of objective world: one "looks as if" it contains only forward causation, the other ``looks as if'' it involves a mix of backward and forward causation. This clarifies the objective core of an advanced action interpretation of QM, and shows that there is an independent symmetry argument in favour of the approach.

2011 - Physical Review A
Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction

How would the world appear to us if its ontology was that of classical mechanics but every agent faced a restriction on how much they could come to know about the classical state? We show that in most respects, it would appear to us as quantum. The statistical theory of classical mechanics, which specifies how probability distributions over phase space evolve under Hamiltonian evolution and under measurements, is typically called Liouville mechanics, so the theory we explore here is Liouville mechanics with an epistemic restriction. The particular epistemic restriction we posit as our foundational postulate specifies two constraints. The first constraint is a classical analogue of Heisenberg's uncertainty principle -- the second-order moments of position and momentum defined by the phase-space distribution that characterizes an agent's knowledge are required to satisfy the same constraints as are satisfied by the moments of position and momentum observables for a quantum state. The second constraint is that the distribution should have maximal entropy for the given moments. Starting from this postulate, we derive the allowed preparations, measurements and transformations and demonstrate that they are isomorphic to those allowed in Gaussian quantum mechanics and generate the same experimental statistics. We argue that this reconstruction of Gaussian quantum mechanics constitutes additional evidence in favour of a research program wherein quantum states are interpreted as states of incomplete knowledge, and that the phenomena that do not arise in Gaussian quantum mechanics provide the best clues for how one might reconstruct the full quantum theory.

1997 - quant-ph/9709031
Measurement of time of arrival in quantum mechanics

It is argued that the time of arrival cannot be precisely defined and measured in quantum mechanics. By constructing explicit toy models of a measurement, we show that for a free particle it cannot be measured more accurately then $\ensuremath{\Delta}{t}_{A}\ensuremath{\sim}{1/E}_{k},$ where ${E}_{k}$ is the initial kinetic energy of the particle. With a better accuracy, particles reflect off the measuring device, and the resulting probability distribution becomes distorted. It is shown that a time-of-arrival operator cannot exist, and that approximate time-of-arrival operators do not correspond to the measurements considered here.

1970 - Physical Review D
CALCULUS FOR FUNCTIONS OF NONCOMMUTING OPERATORS AND GENERAL PHASE-SPACE METHODS IN QUANTUM MECHANICS. I. MAPPING THEOREMS AND ORDERING OF FUNCTIONS OF NONCOMMUTING OPERATORS.

A new calculus for functions of noncommuting operators is developed, based on the notion of mapping of functions of operators onto $c$-number functions. The class of linear mappings, each member of which is characterized by an entire analytic function of two complex variables, is studied in detail. Closed-form solutions for such mappings and for the inverse mappings are obtained and various properties of these mappings are studied. It is shown that the most commonly occurring rules of association between operators and $c$-numbers (the Weyl, the normal, the antinormal, the standard, and the antistandard rules) belong to this class and are, in fact, the simplest ones in a clearly defined sense. It is shown further that the problem of expressing an operator in an ordered form according to some prescribed rule is equivalent to an appropriate mapping of the operator on a $c$-number space. The theory provides a systematic technique for the solution of numerous quantum-mechanical problems that were treated in the past by ad hoc methods, and it furnishes a new approach to many others. This is illustrated by a number of examples relating to mappings and ordering of operators.

2010
Principles of Quantum Mechanics

Reviews from the First Edition: 'An excellent text? The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner' - ("American Scientist"). 'No matter how gently one introduces students to the concept of Dirac's bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of' - ("Physics Bulletin").Reviews of the Second Edition: 'This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details - all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. It would be particularly useful to beginning students and those in allied areas like quantum chemistry' - ("Mathematical Reviews").R. Shankar has introduced major additions and updated key presentations in this second edition of "Principles of Quantum Mechanics". New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include: clear, accessible treatment of underlying mathematics; a review of Newtonian, Lagrangian, and Hamiltonian mechanics; student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates; and, unsurpassed coverage of path integrals and their relevance in contemporary physics.The requisite text for advanced undergraduate- and graduate-level students, "Principles of Quantum Mechanics, Second Edition" is fully referenced and is supported by many exercises and solutions. The book's self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

1965
Relativistic Quantum Mechanics

In this text the authors develop a propagator theory of Dirac particles, photons, and Klein-Gordon mesons and per- form a series of calculations designed to illustrate various useful techniques and concepts in electromagnetic, weak, and strong interactions. these include defining and implementing the renormalization program and evaluating effects of radia- tive corrections, such as the Lamb shift, in low-order calculations. The necessary background for the book is pro- vided by a course in nonrelativistic quantum mechanics at the general level of Schiff's text, QUANTUM MECHANICS.

Mental States Follow Quantum Mechanics During Perception and Cognition of Ambiguous Figures

Andrei Khrennikov
|
Joseph P. Zbilut
|
Elio Conte
|
Orlando Todarello
|
Antonio Federici
|
Leonardo Mendolicchio

Abstract:Processes undergoing quantum mechanics exhibit quantum interference effects. In this case, quantum probabilities result to be different from classical ones because they contain an additional so-called quantum interference term. We use ambiguous figures to analyse if during perception-cognition by human subjects we can observe violation of the classical probability field and the presence of quantum interference. The experiments, conducted on a group of 256 subjects, evidence that we indeed have such a quantum effect. Therefore, mental states, during perception and cognition of ambiguous figures, appear to follow quantum mechanics.

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