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Classical and Quantum Dynamics

from Classical Paths to Path Integrals

  • Textbook
  • © 1992

Overview

Authors:
  1. Walter Dittrich

    1. Institut für Theoretische Physik, Universität Tübingen, Tübingen, Fed. Rep. of Germany

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  2. Martin Reuter

    1. Institut für Theoretische Physik, Universität Hannover, Hannover 1, Fed. Rep. of Germany

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (31 chapters)

  1. Propagators for Particles in an External Magnetic Field

    • Walter Dittrich, Martin Reuter
    Pages 225-229

  2. Simple Applications of Propagator Functions

    • Walter Dittrich, Martin Reuter
    Pages 231-246

  3. The WKB Approximation

    • Walter Dittrich, Martin Reuter
    Pages 247-256

  4. Partition Function for the Harmonic Oscillator

    • Walter Dittrich, Martin Reuter
    Pages 257-262

  5. Introduction to Homotopy Theory

    • Walter Dittrich, Martin Reuter
    Pages 263-267

  6. Classical Chern-Simons Mechanics

    • Walter Dittrich, Martin Reuter
    Pages 269-279

  7. Semiclassical Quantization

    • Walter Dittrich, Martin Reuter
    Pages 281-286

  8. The “Maslov Anomaly” for the Harmonic Oscillator

    • Walter Dittrich, Martin Reuter
    Pages 287-294

  9. Maslov Anomaly and the Morse Index Theorem

    • Walter Dittrich, Martin Reuter
    Pages 295-300

  10. Berry’s Phase

    • Walter Dittrich, Martin Reuter
    Pages 301-309

  11. Classical Analogues to Berry’s Phase

    • Walter Dittrich, Martin Reuter
    Pages 311-322

  12. Berry Phase and Parametric Harmonic Oscillator

    • Walter Dittrich, Martin Reuter
    Pages 323-335

  13. Back Matter

    Pages 337-341
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About this book

In the past 10 to 15 years, the quantum leap in understanding of nonlinear dynamics has radically changed the frame of reference of physicists contemplating such systems. This book treats classical and quantum mechanics using an approach as introduced by nonlinear Hamiltonian dynamics and path integral methods. It is written for graduate students who want to become familiar with the more advancedcomputational strategies in classical and quantum dynamics. Therefore, worked examples comprise a large part of the text. While the first half of the book lays the groundwork for a standard course, the second half, with its detailed treatment of the time-dependent oscillator, classical and quantum Chern-Simons mechanics, the Maslov anomaly and the Berry phase, willacquaint the reader with modern topological methods that have not as yet found their way into the textbook literature.

Authors and Affiliations

  • Institut für Theoretische Physik, Universität Tübingen, Tübingen, Fed. Rep. of Germany

    Walter Dittrich

  • Institut für Theoretische Physik, Universität Hannover, Hannover 1, Fed. Rep. of Germany

    Martin Reuter

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