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Quantum Mechanics on Phase Space

  • Book
  • © 1996

Overview

Authors:
  1. Franklin E. Schroeck

    1. Department of Mathematics, Florida Atlantic University, Boca Raton, USA

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Part of the book series: Fundamental Theories of Physics (FTPH, volume 74)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Basic Quantum Theory and the Necessity for Its Revision

    • Franklin E. Schroeck Jr.
    Pages 1-133

  3. Basic Experiments Suggest Generalizing Quantum Mechanics

    • Franklin E. Schroeck Jr.
    Pages 134-289

  4. Construction of Quantum Mechanics on Phase Space

    • Franklin E. Schroeck Jr.
    Pages 290-512

  5. Consequences of Formulating Quantum Mechanics on Phase Space

    • Franklin E. Schroeck Jr.
    Pages 513-567

  6. Foundational Aspects

    • Franklin E. Schroeck Jr.
    Pages 568-626

  7. Back Matter

    Pages 627-672
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Keywords

About this book

In this monograph, we shall present a new mathematical formulation of quantum theory, clarify a number of discrepancies within the prior formulation of quantum theory, give new applications to experiments in physics, and extend the realm of application of quantum theory well beyond physics. Here, we motivate this new formulation and sketch how it developed. Since the publication of Dirac's famous book on quantum mechanics [Dirac, 1930] and von Neumann's classic text on the mathematical foundations of quantum mechanics two years later [von Neumann, 1932], there have appeared a number of lines of development, the intent of each being to enrich quantum theory by extra­ polating or even modifying the original basic structure. These lines of development have seemed to go in different directions, the major directions of which are identified here: First is the introduction of group theoretical methods [Weyl, 1928; Wigner, 1931] with the natural extension to coherent state theory [Klauder and Sudarshan, 1968; Peremolov, 1971]. The call for an axiomatic approach to physics [Hilbert, 1900; Sixth Problem] led to the development of quantum logic [Mackey, 1963; Jauch, 1968; Varadarajan, 1968, 1970; Piron, 1976; Beltrametti & Cassinelli, 1981], to the creation of the operational approach [Ludwig, 1983-85, 1985; Davies, 1976] with its application to quantum communication theory [Helstrom, 1976; Holevo, 1982), and to the development of the C* approach [Emch, 1972]. An approach through stochastic differential equations ("stochastic mechanics") was developed [Nelson, 1964, 1966, 1967].

Authors and Affiliations

  • Department of Mathematics, Florida Atlantic University, Boca Raton, USA

    Franklin E. Schroeck

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