Quantum Reprogramming

Ensembles and Single Systems: A Two-Tier Approach to Quantum Mechanics

  • Authors
  • Evert Jan Post

Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 181)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Introductory Remarks

    1. Evert Jan Post
      Pages 1-14
  3. The Copenhagen Era

    1. Front Matter
      Pages 15-15
    2. Evert Jan Post
      Pages 16-34
    3. Evert Jan Post
      Pages 35-59
    4. Evert Jan Post
      Pages 60-73
    5. Evert Jan Post
      Pages 74-83
  4. A Sommerfeld-De Rham View of Single Systems

    1. Front Matter
      Pages 84-84
    2. Evert Jan Post
      Pages 85-118
    3. Evert Jan Post
      Pages 119-125
    4. Evert Jan Post
      Pages 126-143
    5. Evert Jan Post
      Pages 144-150
    6. Evert Jan Post
      Pages 151-168
    7. Evert Jan Post
      Pages 169-187
  5. An Attempt at Cohomological Synthesis

    1. Front Matter
      Pages 188-188
    2. Evert Jan Post
      Pages 189-197
    3. Evert Jan Post
      Pages 198-223
    4. Evert Jan Post
      Pages 224-238
  6. Ramifications of the Two-Tier View of Q.M.

    1. Front Matter
      Pages 239-239

About this book

Introduction

Many, perhaps most textbooks of quantum mechanics present a Copenhagen, single system angle; fewer present the subject matter as an instrument for treating ensembles, but the two methods have been silently coexisting since the mid-Thirties. This lingering dichotomy of purpose for a major physical discipline has much shrouded further insights into the foundations of quantum theory.
Quantum Reprogramming resolves this long-standing dichotomy by examining the mutual relation between single systems and ensembles, assigning each its own tools for treating the subject at hand: i.e., Schrödinger-Dirac methods for ensembles versus period integrals for single systems.
A unified treatment of integer and fractional quantum Hall effects and a finite description of the electron's anomalies are mentioned as measures of justification for the chosen procedure of resolving an old-time dichotomy. The methods of presentation are, in part, elementary, with repetitive references needed to delineate differences with respect to standard methods. The parts on period integrals are developed with a perspective on elementary methods in physics, thus leading up to some standard results of de Rham theory and algebraic topology.
Audience: Students of physics, mathematics, philosophers as well as outsiders with a general interest in the conceptual development of physics will find useful reading in these pages, which will stimulate further inquiry and study.

Keywords

Algebraic topology Quantum Hall effect cohomology homology quantum mechanics

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8410-4
  • Copyright Information Springer Science+Business Media B.V. 1995
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4575-1
  • Online ISBN 978-94-015-8410-4
  • Series Print ISSN 0068-0346
  • About this book