Time-Dependent Perturbation Theory
Except for the problem of magnetic resonance, we have avoided studying phenomena governed by a time-dependent Hamiltonian.
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Principles of Quantum Mechanics SECOND EDITION
R. Shankar Yale University New Haven, Connecticut
~Springer
Library of Congress Cataloging–in–Publication Data Shankar, Ramamurti. Principles of quantum mechanics / R. Shankar. 2nd ed. p. cm. Includes bibliographical references and index. ISBN 0-306-44790-8 1. Quantum theory. I. Title. QC174. 12.S52 1994 530. 1’2–dc20
94–26837 CIP
ISBN 978-1-4757-0578-2 ISBN 978-1-4757-0576-8 (eBook) DOI: 10.1007/978-1-4757-0576-8 © 1994, 1980 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 19 18 springer.com
(corrected printing, 2008)
To
My
Parent~
and to Uma, Umesh, Ajeet, Meera, and Maya
Preface to the Second Edition Over the decade and a half since I wrote the first edition, nothing has altered my belief in the soundness of the overall approach taken here. This is based on the response of teachers, students, and my own occasional rereading of the book. I was generally quite happy with the book, although there were portions where I felt I could have done better and portions which bothered me by their absence. I welcome this opportunity to rectify all that. Apart from small improvements scattered over the text, there are three major changes. First, I have rewritten a big chunk of the mathematical introduction in Chapter 1. Next, I have added a discussion of time-reversal in variance. I don't know how it got left out the first time-1 wish I could go back and change it. The most important change concerns the inclusion of Chaper 21, "Path Integrals: Part II." The first edition already revealed my partiality for this subject by having a chapter devoted to it, which was quite unusual in those days. In this one, I have cast off all restraint and gone all out to discuss many kinds of path integrals and their uses. Whereas in Chapter 8 the path integral recipe was simply given, here I start by deriving it. I derive the configuration space integral (the usual Feynman integral), phase space integral, and (oscillator) coherent state integral. I discuss two applications: the derivation and application of the Berry phase and a study of the lowest Landau level with an eye on the quantum H.all effect. The relevance of these topics is unquestionable. This is followed by a section of imaginary time path integrals~ its description of tunnelin
