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Chaos in Classical and Quantum Mechanics

  • Textbook
  • © 1990

Overview

Authors:
  1. Martin C. Gutzwiller

    1. IBM T.J. Watson Research Center, Yorktown Heights, USA

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Part of the book series: Interdisciplinary Applied Mathematics (IAM, volume 1)

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Introduction

    • Martin C. Gutzwiller
    Pages 1-4

  3. The Mechanics of Lagrange

    • Martin C. Gutzwiller
    Pages 5-18

  4. The Mechanics of Hamilton and Jacobi

    • Martin C. Gutzwiller
    Pages 19-29

  5. Integrable Systems

    • Martin C. Gutzwiller
    Pages 30-44

  6. The Three-Body Problem: Moon — Earth — Sun

    • Martin C. Gutzwiller
    Pages 45-57

  7. Three Methods of Solution

    • Martin C. Gutzwiller
    Pages 58-74

  8. Periodic Orbits

    • Martin C. Gutzwiller
    Pages 75-86

  9. The Surface of Section

    • Martin C. Gutzwiller
    Pages 87-98

  10. Models of the Galaxy and of Small Molecules

    • Martin C. Gutzwiller
    Pages 99-115

  11. Soft Chaos and the KAM Theorem

    • Martin C. Gutzwiller
    Pages 116-141

  12. Entropy and Other Measures of Chaos

    • Martin C. Gutzwiller
    Pages 142-155

  13. The Anisotropic Kepler Problem

    • Martin C. Gutzwiller
    Pages 156-172

  14. The Transition from Classical to Quantum Mechanics

    • Martin C. Gutzwiller
    Pages 173-193

  15. The New World of Quantum Mechanics

    • Martin C. Gutzwiller
    Pages 194-206

  16. The Quantization of Integrable Systems

    • Martin C. Gutzwiller
    Pages 207-230

  17. Wave Functions in Classically Chaotic Systems

    • Martin C. Gutzwiller
    Pages 231-253

  18. The Energy Spectrum of a Classically Chaotic System

    • Martin C. Gutzwiller
    Pages 254-281

  19. The Trace Formula

    • Martin C. Gutzwiller
    Pages 282-321

  20. The Diamagnetic Kepler Problem

    • Martin C. Gutzwiller
    Pages 322-339
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Keywords

About this book

Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.

Authors and Affiliations

  • IBM T.J. Watson Research Center, Yorktown Heights, USA

    Martin C. Gutzwiller

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