Advertisement

Quantum Mechanics on Phase Space

  • Franklin E. SchroeckJr.

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

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Franklin E. Schroeck Jr.
    Pages 1-133
  3. Franklin E. Schroeck Jr.
    Pages 134-289
  4. Franklin E. Schroeck Jr.
    Pages 290-512
  5. Franklin E. Schroeck Jr.
    Pages 513-567
  6. Franklin E. Schroeck Jr.
    Pages 568-626
  7. Back Matter
    Pages 627-672

About this book

Introduction

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].

Keywords

Group representation Lattice Observable Representation theory neuroscience perception quantum mechanics science

Authors and affiliations

  • Franklin E. SchroeckJr.
    • 1
  1. 1.Department of MathematicsFlorida Atlantic UniversityBoca RatonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-2830-0
  • Copyright Information Springer Science+Business Media B.V. 1996
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4639-0
  • Online ISBN 978-94-017-2830-0
  • Buy this book on publisher's site
Industry Sectors
Electronics
IT & Software
Consumer Packaged Goods
Aerospace