Advertisement

Adiabatic Perturbation Theory in Quantum Dynamics

  • Authors
  • Stefan¬†Teufel

Part of the Lecture Notes in Mathematics book series (LNM, volume 1821)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Stefan Teufel
    Pages 1-31
  3. Stefan Teufel
    Pages 33-69
  4. Stefan Teufel
    Pages 71-104
  5. Stefan Teufel
    Pages 105-140
  6. Stefan Teufel
    Pages 141-171
  7. Stefan Teufel
    Pages 173-201
  8. Stefan Teufel
    Pages 203-224
  9. Stefan Teufel
    Pages 225-234
  10. Back Matter
    Pages 235-236

About this book

Introduction

Separation of scales plays a fundamental role in the understanding of the dynamical behaviour of complex systems in physics and other natural sciences. A prominent example is the Born-Oppenheimer approximation in molecular dynamics. This book focuses on a recent approach to adiabatic perturbation theory, which emphasizes the role of effective equations of motion and the separation of the adiabatic limit from the semiclassical limit.

A detailed introduction gives an overview of the subject and makes the later chapters accessible also to readers less familiar with the material. Although the general mathematical theory based on pseudodifferential calculus is presented in detail, there is an emphasis on concrete and relevant examples from physics. Applications range from molecular dynamics to the dynamics of electrons in a crystal and from the quantum mechanics of partially confined systems to Dirac particles and nonrelativistic QED.

Keywords

Pseudodifferential Operators Quantum mechanics adiabatic limit calculus equation semiclassical limit

Bibliographic information

  • DOI https://doi.org/10.1007/b13355
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-40723-2
  • Online ISBN 978-3-540-45171-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site