Canonical Adiabatic Theory

In the present chapter we are concerned with systems, the change of which — with the exception of a single degree of freedom — should proceed slowly. (Compare the pertinent remarks about ε as slow parameter in Chap. 7.) Accordingly, the Hamiltonian reads:

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Advanced Texts in Physics This program of advanced texts covers a broad spectrum of topics which are of current and emerging interest in physics. Each book provides a comprehensive and yet accessible introduction to a field at the forefront of modern research. As such, these texts are intended for senior undergraduate and graduate students at the MS and PhD level; however, research scientists seeking an introduction to particular areas of physics will also benefit from the titles in this collection.

Walter Dittrich

Martin Reuter

Classical and Quantum Dynamics From Classical Paths to Path Integrals

Third Edition

Springer

Prof. Dr. W . Dittrich

Prof. Dr. Martin Reuter

University of Tübingen Institute of Theoretical Physics Auf der Morgenstelle 14 72076 Tübingen Germany

University of Mainz Institute of Physics Staudinger Weg 7 55099 Mainz Germany e-mail: [email protected]

Library of Congress Cataloging-in-Publication Data Dittrich, Walter. Classical and quantum dynamics : from classical paths to path integrals / Walter Dittrich, Martin Reuter.— 3. ed. p.cm.— (Advanced texts in physics, ISSN 1439-2674) Orginally published: Classical and quatum dynamics. 2nd corr. and enl. ed. Berlin ; New York : SpringerVerlag, C1994. Includes bibliographical references and index ISBN 978-3-540-42066-8 ISBN 978-3-642-56430-7 (eBook) DOI 10.1007/978-3-642-56430-7

I. Quantum theory. 2. Nonlinear theories. 3. Harniltounian system. 4. Path integrals. I. Reuter, Martin, 1958II. Titel. III Series. QC174.12.D59 2001 530.12—dc2i 2001031421

ISSN 1439-2674 ISBN 978-3-540-42066-8 This work is subject to copyright. A l l rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law.

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Preface to the Third Edition

In this third edition the major purposes and emphasis are still the same, but there are extensive addition s. These consist mainly