Search results for 'matrix mechanics' (try it on Scholar)

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  1. Slobodan Perovic (2008). Why Were Matrix Mechanics and Wave Mechanics Considered Equivalent? Studies in History and Philosophy of Science Part B 39 (2):444-461.score: 180.0
    A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schrödinger's 1926 proof, a myth. Schrödinger supposedly failed to prove isomorphism, or even a weaker equivalence (“Schrödinger-equivalence”) of the mathematical structures of the two theories; developments in the early 1930s, especially the work of mathematician von Neumann provided sound proof of mathematical equivalence. The alleged agreement about the Copenhagen Interpretation, predicated (...)
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  2. Slobodan Perovic (2008). Why Were Two Theories (Matrix Mechanics and Wave Mechanics) Deemed Logically Distinct, and yet Equivalent, in Quantum Mechanics? In Christopher Lehrer (ed.), First Annual Conference in the Foundations and History of Quantum Physics. Max Planck Institute for History of Science.score: 180.0
    A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schrödinger’s 1926 proof, a myth. Schrödinger supposedly failed to achieve the goal of proving isomorphism of the mathematical structures of the two theories, while only later developments in the early 1930s, especially the work of mathematician John von Neumman (1932) provided sound proof of equivalence. The alleged agreement about the Copenhagen (...)
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  3. Michel Janssen, Van Vleck and Slater: Two Americans on the Road to Matrix Mechanics.score: 120.0
    I relate the story of how matrix mechanics grew out of the treatment of optical dispersion in the old quantum theory, paying special attention to the contributions of the American theoretical physicists John H. Van Vleck and John C. Slater. Van Vleck shares the credit with Max Born for being the first to publish a full derivation of the crucial Kramers dispersion formula using Bohr’s correspondence principle. Slater was one of the architects of the short-lived but influential Bohr-Kramers-Slater (...)
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  4. Authur A. Frost (1975). Matrix Formulation of Special Relativity in Classical Mechanics and Electromagnetic Theory. Foundations of Physics 5 (4):619-641.score: 96.0
    The two-component spinor theory of van der Waerden is put into a convenient matrix notation. The mathematical relations among various types of matrices and the rule for forming covariant expressions are developed. Relativistic equations of classical mechanics and electricity and magnetism are expressed in this notation. In this formulation the distinction between time and space coordinates in the four-dimensional space-time continuum falls out naturally from the assumption that a four-vector is represented by a Hermitian matrix. The indefinite (...)
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  5. Gui Lu Long, Yi-Fan Zhou, Jia-Qi Jin, Yang Sun & Hai-Woong Lee (2006). Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix. Foundations of Physics 36 (8):1217-1243.score: 90.0
    We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in (...)
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  6. Gabriele Brandstettter (2005). The Code of Terpsichore the Dance Theory of Carlo Blasis: Mechanics as the Matrix of Grace. Topoi 24 (1):67-79.score: 78.0
    The essay examines both the dances and the dance notation of renowned nineteenth century choreographer Carlo Blasis. It looks in detail at Blasis major treatise The Code of Terpsichore in an effort to evaluate how Blasis linked a science of movement to a conception of the body oriented around the prevailing aesthetics informing all of the fine arts. Identifying Blasis as both a philosopher and a mechanist, this essay analyzes his approach to teaching basic ballet vocabulary, and in particular the (...)
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  7. Diego L. Rapoport (2011). Surmounting the Cartesian Cut Through Philosophy, Physics, Logic, Cybernetics, and Geometry: Self-Reference, Torsion, the Klein Bottle, the Time Operator, Multivalued Logics and Quantum Mechanics. [REVIEW] Foundations of Physics 41 (1):33-76.score: 72.0
    In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to (...)
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  8. Detlef Dürr, Sheldon Goldstein, Roderich Tumulka & Nino Zanghí (2005). On the Role of Density Matrices in Bohmian Mechanics. Foundations of Physics 35 (3):449-467.score: 66.0
  9. L. De la Peña, A. Valdés-Hernández & A. M. Cetto (2009). Quantum Mechanics as an Emergent Property of Ergodic Systems Embedded in the Zero-Point Radiation Field. Foundations of Physics 39 (11):1240-1272.score: 54.0
    The present paper reveals (non-relativistic) quantum mechanics as an emergent property of otherwise classical ergodic systems embedded in a stochastic vacuum or zero-point radiation field (zpf). This result provides a theoretical basis for understanding recent numerical experiments in which a statistical analysis of an atomic electron interacting with the zpf furnishes the quantum distribution for the ground state of the H atom. The action of the zpf on matter is essential within the present approach, but it is the ergodic (...)
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  10. August Stern (1992). Matrix Logic and Mind: A Probe Into a Unified Theory of Mind and Matter. Distributors for the U.S. And Canada, Elsevier Science Pub. Co..score: 54.0
    In this revolutionary work, the author sets the stage for the science of the 21st Century, pursuing an unprecedented synthesis of fields previously considered unrelated. Beginning with simple classical concepts, he ends with a complex multidisciplinary theory requiring a high level of abstraction. The work progresses across the sciences in several multidisciplinary directions: Mathematical logic, fundamental physics, computer science and the theory of intelligence. Extraordinarily enough, the author breaks new ground in all these fields. In the field of fundamental physics (...)
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  11. C. Wetterich (2012). Probabilistic Time. Foundations of Physics 42 (11):1384-1443.score: 48.0
    The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions p τ (t) at a given time t obtain by integrating out the past and future. We discuss all-time probability distributions that realize a unitary time evolution as described by rotations of the real wave function $q_{\tau}(t)=\pm \sqrt{p_{\tau}(t)}$ . We establish a map to quantum physics and the Schrödinger equation. Suitable classical observables are mapped to quantum operators. The non-commutativity of the operator product is (...)
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  12. Carlos M. Madrid Casado (2011). Sr. Realista estructural, tenemos un problema: la carga ontológica de las matemáticas. Principia 14 (2):201-209.score: 48.0
    The aim of this note is to undermine structural realism by testing the soundness of its main claim. If scientific theories represent the structure of the world, structural realism needs a general account of representation. Representation is the crux of structural realism, because structure/ontology distinction collapses. Mathematical structures are ontologyladen. DOI:10.5007/1808-1711.2010v14n2p201.
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  13. Michael Silberstein, W. M. Stuckey & Michael Cifone, An Argument for 4d Blockworld From a Geometric Interpretation of Non-Relativistic Quantum Mechanics.score: 42.0
    We use a new, distinctly “geometrical” interpretation of non-relativistic quantum mechanics (NRQM) to argue for the fundamentality of the 4D blockworld ontology. We argue for a geometrical interpretation whose fundamental ontology is one of spacetime relations as opposed to constructive entities whose time-dependent behavior is governed by dynamical laws. Our view rests on two formal results: Kaiser (1981 & 1990), Bohr & Ulfbeck (1995) and Anandan, (2003) showed independently that the Heisenberg commutation relations of NRQM follow from the relativity (...)
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  14. D. Bohm & B. J. Hiley (1996). Statistical Mechanics and the Ontological Interpretation. Foundations of Physics 26 (6):823-846.score: 42.0
    To complete our ontological interpretation of quantum theory we have to conclude a treatment of quantum statistical mechanics. The basic concepts in the ontological approach are the particle and the wave function. The density matrix cannot play a fundamental role here. Therefore quantum statistical mechanics will require a further statistical distribution over wave functions in addition to the distribution of particles that have a specified wave function. Ultimately the wave function of the universe will he required, but (...)
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  15. S. Bergia, F. Cannata, A. Cornia & R. Livi (1980). On the Actual Measurability of the Density Matrix of a Decaying System by Means of Measurements on the Decay Products. Foundations of Physics 10 (9-10):723-730.score: 42.0
    The density matrix ρ describing a decaying system can be expressed in terms of correlations among observables belonging to the subsystems. Due to this structure and to the difficulties in measuring higher rank tensors of decay products for a single decay event, it is found that the mean value of ρ cannot be determined, in general, from measurements on the decay products. We also discuss the consequences of this conclusion as far as tests of quantum mechanics are concerned.
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  16. H. S. Green (1978). Quantum Mechanics of Space and Time. Foundations of Physics 8 (7-8):573-591.score: 42.0
    A formulation of relativistic quantum mechanics is presented independent of the theory of Hilbert space and also independent of the hypothesis of spacetime manifold. A hierarchy is established in the nondistributive lattice of physical ensembles, and it is shown that the projections relating different members of the hierarchy form a semigroup. It is shown how to develop a statistical theory based on the definition of a statistical operator. Involutions defined on the matrix representations of the semigroup are interpreted (...)
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  17. O. Costa de Beauregard (1988). On the Zigzagging Causility Model of EPR Correlations and on the Interpretation of Quantum Mechanics. Foundations of Physics 18 (9):913-938.score: 42.0
    Being formalized inside the S-matrix scheme, the zigzagging causility model of EPR correlations has full Lorentz and CPT invariance. EPR correlations, proper or reversed, and Wheeler's smoky dragon metaphor are respectively pictured in spacetime or in the momentum-energy space, as V-shaped, A-shaped, or C-shaped ABC zigzags, with a summation at B over virtual states |B〉 〈B|. An exact “correspondence” exists between the Born-Jordan-Dirac “wavelike” algebra of transition amplitudes and the 1774 Laplace algebra of conditional probabilities, where the intermediate summations (...)
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  18. James Ax (1976). Group-Theoretic Treatment of the Axioms of Quantum Mechanics. Foundations of Physics 6 (4):371-399.score: 42.0
    This axiomatization is based on the observation that ifG is the group of automorphisms of the states (induced, e.g., by suitable evolutions), then we can define a spherical function by mapping each element ofG to the matrix of its transition probabilities. Starting from five physically conservative axioms, we utilize the correspondence between spherical functions and representations to apply the structure theory for compact Lie groups and their orbits in representation spaces to arrive at the standard complex Hilbert space structure (...)
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  19. OR Shenker (1999). Is - Ktr(Ln) the Entropy in Quantum Mechanics. British Journal for the Philosophy of Science 50 (1):33-48.score: 42.0
    In quantum mechanics, the expression for entropy is usually taken to be -kTr(ln), where is the density matrix. The convention first appears in Von Neumann's Mathematical Foundations of Quantum Mechanics. The argument given there to justify this convention is the only one hitherto offered. All the arguments in the field refer to it at one point or another. Here this argument is shown to be invalid. Moreover, it is shown that, if entropy is -kTr(ln), then perpetual motion (...)
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  20. M. Cini, M. De Maria, G. Mattioli & F. Nicolò (1979). Wave Packet Reduction in Quantum Mechanics: A Model of a Measuring Apparatus. [REVIEW] Foundations of Physics 9 (7-8):479-500.score: 42.0
    We investigate the problem of “wave packet reduction” in quantum mechanics by solving the Schrödinger equation for a system composed of a model measuring apparatusM interacting with a microscopic objects. The “instrument” is intended to be somewhat more realistic than others previously proposed, but at the same time still simple enough to lead to an explicit solution for the time-dependent density matrix. It turns out that,practically, everything happens as if the wave packet reduction had occurred. This is a (...)
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  21. L. Diósi (1990). Landau's Density Matrix in Quantum Electrodynamics. Foundations of Physics 20 (1):63-70.score: 42.0
    This paper is devoted to Landau's concept of the problem of damping in quantum mechanics. It shows that Landau's density matrix formalism should survive in the context of modern quantum electrodynamics. The correct generalized master equation has been derived for the reduced dynamics of the charges. The recent relativistic theory of spontaneous emission becomes reproducible.
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  22. Ashot S. Gevorkyan (2011). Nonrelativistic Quantum Mechanics with Fundamental Environment. Foundations of Physics 41 (3):509-515.score: 42.0
    Spontaneous transitions between bound states of an atomic system, “Lamb Shift” of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations (fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system “quantum system (QS) + FE” is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ⊗ (...)
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  23. Bert Schroer (2010). Localization and the Interface Between Quantum Mechanics, Quantum Field Theory and Quantum Gravity I. Studies in History and Philosophy of Science Part B 41 (2):104-127.score: 36.0
    It is shown that there are significant conceptual differences between QM and QFT which make it difficult to view the latter as just a relativistic extension of the principles of QM. At the root of this is a fundamental distiction between Born-localization in QM (which in the relativistic context changes its name to Newton–Wigner localization) and modular localization which is the localization underlying QFT, after one separates it from its standard presentation in terms of field coordinates. The first comes with (...)
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  24. Diego L. Rapoport (2009). Surmounting the Cartesian Cut with Philosophy, Physics, Cybernetics and Geometry; Self.Reference, Torsion, the Klein Bottle, Multivalued Logics and Quantum Mechanics. foundations of physics 39 (09).score: 36.0
    In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology -after Merleau-Ponty, Heidegger and Rosen- and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further (...)
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  25. Eamonn Healy (2011). Heisenberg's Chemical Legacy: Resonance and the Chemical Bond. [REVIEW] Foundations of Chemistry 13 (1):39-49.score: 30.0
    Heisenberg’s explanation of how two coupled oscillators exchange energy represented a dramatic success for his new matrix mechanics. As matrix mechanics transmuted into wave mechanics, resulting in what Heisenberg himself described as …an extraordinary broadening and enrichment of the formalism of the quantum theory , the term resonance also experienced a corresponding evolution. Heitler and London’s seminal application of wave mechanics to explain the quantum origins of the covalent bond, combined with Pauling’s characterization of (...)
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  26. Alisa Bokulich, Three Puzzles About Bohr's Correspondence Principle.score: 30.0
    Niels Bohr’s “correspondence principle” is typically believed to be the requirement that in the limit of large quantum numbers (n→∞) there is a statistical agreement between the quantum and classical frequencies. A closer reading of Bohr’s writings on the correspondence principle, however, reveals that this interpretation is mistaken. Specifically, Bohr makes the following three puzzling claims: First, he claims that the correspondence principle applies to small quantum numbers as well as large (while the statistical agreement of frequencies is only for (...)
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  27. Henry Stapp, Schroedinger's Cat.score: 30.0
    Erwin Schroedinger and Werner Heisenberg were the originators of two approaches, known respectively as “wave mechanics” and “matrix mechanics”, to what is now called “quantum mechanics’ or “quantum theory”. The two approaches appear to be extremely different, both in their technical forms, and in their philosophical underpinnings. Heisenberg arrived to his theory by effectively renouncing the idea of trying to represent a physical system, such as a hydrogen atom for example, as a structure in space-time, but (...)
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  28. Anthony Duncan & Michel Janssen, On the Verge of Umdeutung in Minnesota: Van Vleck and the Correspondence Principle.score: 30.0
    In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck used Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum formulae for the emission, absorption, and dispersion of radiation. The paper is similar but in many ways superior to the well-known paper by Kramers and Heisenberg published the following year that is widely credited (...)
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  29. Linda Wessels (1980). What Was Born's Statistical Interpretation? PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:187 - 200.score: 30.0
    The statistical interpretation introduced by Born in mid-1926 is not the interpretation now associated with his name. Born's own understanding of that interpretation is revealed by looking at some of its roots in Born's earlier work with Franck on collisions (fall, 1924), his collaboration with Jordan on that topic (early 1925), his contributions to matrix mechanics (last half of 1925), his attempt in collaboration with Wiener at an operator formulation of quantum mechanics (early 1926), and at (...)
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  30. O. J. E. Maroney (2005). The Density Matrix in the de Broglie--Bohm Approach. Foundations of Physics 35 (3):493-510.score: 30.0
    If the density matrix is treated as an objective description of individual systems, it may become possible to attribute the same objective significance to statistical mechanical properties, such as entropy or temperature, as to properties such as mass or energy. It is shown that the de Broglie--Bohm interpretation of quantum theory can be consistently applied to density matrices as a description of individual systems. The resultant trajectories are examined for the case of the delayed choice interferometer, for which Bell (...)
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  31. Thomas Bonk (1994). Bemerkungen Zur Interpretation, Bestätigung Und Progressivität der Frühen Matrizenmechanik. Journal for General Philosophy of Science 25 (1):1 - 15.score: 30.0
    Remarks on Interpretation, Confirmation and Progressiveness of Early Matrix Mechanics. Our note discusses a case study in view of questions of theory-choice. We examine the extent to which the first 'complete, consistent exposition' of matrix mechanics in 1925 can be claimed to be reasonably confirmed, well interpreted and fruitful. Various strategies, by means of deductions and otherwise, by Born, Jordan and Heisenberg to establish these claims are critically assessed. It is shown that the outcome of the (...)
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  32. L. Bass (1977). Biological Replication by Quantum Mechanical Interactions. Foundations of Physics 7 (3-4):221-231.score: 30.0
    Wigner's quantum mechanical formulation of the problem of biological replication is examined with special reference to DNA. His necessary condition for replication is that the number of independent equations in his formulation should not exceed the number of unknowns. Explicit hypotheses concerning the relevant collision matrix are proposed without assuming biotonic modifications of quantum mechanics. Schrödinger's description of the gene as a low-temperature solid, combined with the concept of template, is given mathematical expression which fails to satisfy Wigner's (...)
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  33. Yuji Hasegawa (2012). Entanglement Between Degrees of Freedom in a Single-Particle System Revealed in Neutron Interferometry. Foundations of Physics 42 (1):29-45.score: 24.0
    Initially Einstein, Podolsky, and Rosen (EPR) and later Bell shed light on the non-local properties exhibited by subsystems in quantum mechanics. Separately, Kochen and Specker analyzed sets of measurements of compatible observables and found that a consistent coexistence of these results is impossible, i.e., quantum indefiniteness of measurement results. As a consequence, quantum contextuality, a more general concept compared to non-locality, leads to striking phenomena predicted by quantum theory. Here, we report neutron interferometric experiments which investigate entangled states in (...)
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  34. O. Costa de Beauregard (1985). On Some Frequent but Controversial Statements Concerning the Einstein-Podolsky-Rosen Correlations. Foundations of Physics 15 (8):871-887.score: 24.0
    Quite often the compatibility of the EPR correlations with the relativity theory has been questioned; it has been stated that “the first in time of two correlated measurements instantaneously collapses the other subsystem”; it has been suggested that a causal asymmetry is built into the Feynman propagator. However, the EPR transition amplitude, as derived from the S matrix, is Lorentz andCPT invariant; the correlation formula is symmetric in the two measurements irrespective of their time ordering, so that the link (...)
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  35. W. M. Stuckey, Michael Silberstein & Michael Cifone, Reversing the Arrow of Explanation in the Relational Blockworld: Why Temporal Becoming, the Dynamical Brain and the External World Are All "in the Mind".score: 24.0
    We introduce the Relational Blockworld (RBW) as a paradigm for deflating the mysteries associated with quantum non-separability/non-locality and the measurement problem. We begin by describing how the relativity of simultaneity implies the blockworld, which has an explanatory potential subsuming both dynamical and relational explanations. It is then shown how the canonical commutation relations fundamental to non-relativistic quantum mechanics follow from the relativity of simultaneity. Therefore, quantum mechanics has at its disposal the full explanatory power of the blockworld. Quantum (...)
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  36. Herbert J. Bernstein (1999). Simple Version of the Greenberger-Horne-Zeilinger (GHZ) Argument Against Local Realism. Foundations of Physics 29 (4):521-525.score: 24.0
    Here is a simple, clear, useful proof that quantum mechanics contradicts Einstein, Podolsky, and Rosen's local realistic assumptions. It is a variant of the powerful argument first worked out by Daniel Mordechai Greenberger, Michael A. Horne, and Anton Zeilinger. This version uses the eigenstates of two orthogonal spin components for three spin-1/2 particles. No operator or matrix algebra is necessary. A novel discussion of the background and history serves to introduce this proof and to place it in the (...)
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  37. Kin'ya Takahashi & Kensuke S. Ikeda (2001). Complex-Domain Semiclassical Theory: Application to Time-Dependent Barrier Tunneling Problems. [REVIEW] Foundations of Physics 31 (1):177-201.score: 24.0
    Semiclassical theory based upon complexified classical mechanics is developed for periodically time-dependent scattering systems, which are minimal models of multi-dimensional systems. Semiclassical expression of the wave-matrix is derived, which is represented as the sum of the contributions from classical trajectories, where all the dynamical variables as well as the time are extended to the complex-domain. The semiclassical expression is examined by a periodically perturbed 1D barrier system and an excellent agreement with the fully quantum result is confirmed. In (...)
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  38. B. Sakita (1997). Random Matrices, Fermions, Collective Fields, and Universality. Foundations of Physics 27 (11):1519-1525.score: 24.0
    We first relate the random matrix model to a Fokker-Planck Hamiltonian system, such that the correlation functions of the model are expressed as the vacuum expectation values of equal-time products of density operators. We then analyze the universality of the random matrix model by solving the Focker-Planck Hamiltonian system for large N. We use two equivalent methods to do this, namely the method of relating it to a system of interacting fermions in one space dimension and the method (...)
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  39. Asher Peres (1996). Generalized Kochen-Specker Theorem. Foundations of Physics 26 (6):807-812.score: 24.0
    A generalized Kochen-Specker theorem is proved. It is shown that there exist sets of n projection operators, representing n yes-no questions about a quantum system, such that none of the 2″ possible answers is compatible with sum rules imposed by quantum mechanics. Namely, if a subset of commuting projection operators sums up to a matrix having only even or only odd eigenvalues, the number of “yes” answers ought to he even or odd, respectively. This requirement may lead to (...)
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  40. Sheldon Goldstein & Roderich Tumulka, Normal Typicality and Von Neumann's Quantum Ergodic Theorem.score: 24.0
    We discuss the content and significance of John von Neumann’s quantum ergodic theorem (QET) of 1929, a strong result arising from the mere mathematical structure of quantum mechanics. The QET is a precise formulation of what we call normal typicality, i.e., the statement that, for typical large systems, every initial wave function ψ0 from an energy shell is “normal”: it evolves in such a way that |ψt ψt| is, for most t, macroscopically equivalent to the micro-canonical density matrix. (...)
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  41. S. A. Fulling, B.-G. Englert & M. D. Pilloff (2003). Interacting Bosons at Finite Temperature: How Bogolubov Visited a Black Hole and Came Home Again. [REVIEW] Foundations of Physics 33 (1):87-110.score: 24.0
    The structure of the thermal equilibrium state of a weakly interacting Bose gas is of current interest. We calculate the density matrix of that state in two ways. The most effective method, in terms of yielding a simple, explicit answer, is to construct a generating function within the traditional framework of quantum statistical mechanics. The alternative method, arguably more interesting, is to construct the thermal state as a vector state in an artificial system with twice as many degrees (...)
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  42. Peter Braun, Sven Gnutzmann, Fritz Haake, Marek Kuś & Karol Życzkowski (2001). Level Dynamics and Universality of Spectral Fluctuations. Foundations of Physics 31 (4):613-622.score: 24.0
    The spectral fluctuations of quantum (or wave) systems with a chaotic classical (or ray) limit are mostly universal and faithful to random-matrix theory. Taking up ideas of Pechukas and Yukawa we show that equilibrium statistical mechanics for the fictitious gas of particles associated with the parametric motion of levels yields spectral fluctuations of the random-matrix type. Previously known clues to that goal are an appropriate equilibrium ensemble and a certain ergodicity of level dynamics. We here complete the (...)
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  43. L. P. Horwitz & Y. Strauss (1998). Description of Unstable Systems in Relativistic Quantum Mechanics in the Lax-Phillips Theory. Foundations of Physics 28 (10):1607-1616.score: 24.0
    We discuss some of the experimental motivation for the need for semigroup decay laws and the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to (...)
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  44. Philip D. Mannheim (2007). Solution to the Ghost Problem in Fourth Order Derivative Theories. Foundations of Physics 37 (4-5):532-571.score: 24.0
    We present a solution to the ghost problem in fourth order derivative theories. In particular we study the Pais–Uhlenbeck fourth order oscillator model, a model which serves as a prototype for theories which are based on second plus fourth order derivative actions. Via a Dirac constraint method quantization we construct the appropriate quantum-mechanical Hamiltonian and Hilbert space for the system. We find that while the second-quantized Fock space of the general Pais–Uhlenbeck model does indeed contain the negative norm energy eigenstates (...)
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  45. Jan Hilgevoord & Jos Uffink (1991). Uncertainty in Prediction and in Inference. Foundations of Physics 21 (3):323-341.score: 24.0
    The concepts of uncertainty in prediction and inference are introduced and illustrated using the diffraction of light as an example. The close relationship between the concepts of uncertainty in inference and resolving power is noted. A general quantitative measure of uncertainty in inference can be obtained by means of the so-called statistical distance between probability distributions. When applied to quantum mechanics, this distance leads to a measure of the distinguishability of quantum states, which essentially is the absolute value of (...)
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  46. D. M. Appleby (1999). Bohmian Trajectories Post-Decoherence. Foundations of Physics 29 (12):1885-1916.score: 24.0
    The role of the environment in producing the correct classical limit in the Bohm interpretation of quantum mechanics is investigated, in the context of a model of quantum Brownian motion. One of the effects of the interaction is to produce a rapid approximate diagonalisation of the reduced density matrix in the position representation. This effect is, by itself, insufficient to produce generically quasi-classical behaviour of the Bohmian trajectory. However, it is shown that, if the system particle is initially (...)
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  47. A. Amann & H. Atmanspacher (1998). Fluctuations in the Dynamics of Single Quantum Systems. Studies in History and Philosophy of Science Part B 29 (2):151-182.score: 24.0
    The traditional formalism of quantum mechanics is mainly used to describe ensembles of identical systems (with a density-operator formalism) or single isolated systems, but is not capable of describing single open quantum objects with many degrees of freedom showing pure-state stochastic dynamical behaviour. In particular, stochastic 'line-migration' as in single-molecule spectroscopy of defect molecules in a molecular matrix is not adequately described. Starting with the Bohr scenario of stochastic quantum jumps (between strict energy eigenstates), we try to incorporate (...)
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  48. Antoine Royer (1989). Measurement of Quantum States and the Wigner Function. Foundations of Physics 19 (1):3-32.score: 24.0
    In quantum mechanics, the state of an individual particle (or system) is unobservable, i.e., it cannot be determined experimentally, even in principle. However, the notion of “measuring a state” is meaningful if it refers to anensemble of similarly prepared particles, i.e., the question may be addressed: Is it possible to determine experimentally the state operator (density matrix) into which a given preparation procedure puts particles. After reviewing the previous work on this problem, we give simple procedures, in the (...)
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  49. L. E. Ballentine (1992). Can One Detect the State of an Individual System? Foundations of Physics 22 (3):333-342.score: 24.0
    Some interpretations of quantum mechanics regard a mixed quantum state as a ensemble, each individual member of which has a definite but unknown state vector. Other interpretations ascribe a state vector only to anensemble of similarly prepared systems, but not to anindividual. Previous attempts to detect the hypothetical individual state vectors have failed, essentially because the state operator (density matrix) enters the relevant equations linearly. An example from nonlinear dynamics, in which a density matrix enters nonlinearly, is (...)
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  50. Christian Fronsdal (1993). Classical Foundations of Quantum Groups. Foundations of Physics 23 (4):551-569.score: 24.0
    The concept of classical r matrices is developed from a purely canonical standpoint. The final purpose of this work is to bring about a synthesis between recent developments in the theory of integrable systems and the general theory of quantization as a deformation of classical mechanics. The concept of quantization algebra is here dominant; in integrable systems this is the set of dynamical variables that appear in the Lax pair. The nature of this algebra, a solvable Lie algebra in (...)
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