Over the years, I have received some very useful feedback and I thank all those students and teachers who took the time to do so. Students are also expected to consult the references given at the end of the chapter. Since the aim of this chapter is to guide students toward more frontline topics, it is more concise than the rest of the book. I think, would be to lose a wonderful opportunity to expose the student to ideas that are central to many current research topics and to deny them the attendant excitement. (No one I know, myself included, covers the whole book while teaching any fixed group of students.) A realistic option is for the instructor to teach part of Chapter 21 and assign the rest as reading material, as topics for a take-home exams, term papers, etc. How are instructors to deal with this extra chapter given the time constraints? I suggest omitting some material from the earlier chapters. These concepts are extensively used and it seemed a good idea to provide the students who had the wisdom to buy this book with a head start. These were thought to be topics too advanced for a book like this, but I believe this is no longer true. Then I discuss spin coherent state path integrals and path integrals for fermions. An introduction is given to the transfer matrix. This is followed by a section of imaginary time path integralsits description of tunneling, instantons, and symmetry breaking, and its relation to classical and quantum statistical mechanics. The relevance of these topics is unquestionable. 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 Hall effect. I derive the configuration space integral (the usual Feynman integral), phase space integral, and (oscillator) coherent state integral. Whereas in Chapter 8 the path integral recipe was simply given, here I start by deriving it. In this one, I have cast off all restraint and gone all out to discuss many kinds of path integrals and their uses. The most important change concerns the inclusion of Chaper 21, "Path Integrals: Part 11." The first edition already revealed my partiality for this subject by having a chapter devoted to it, which was quite unusual in those days. I don't know how it got left out the first time-I wish I could go back and change it.
Next, I have added a discussion of time-reversal invariance. First, I have rewritten a big chunk of the mathematical introduction in Chapter 1. Apart from small improvements scattered over the text, there are three major changes. I welcome this opportunity to rectify all that. I was generally quite happy with the book, although there were portions where I felt I could havz done better and portions which bothered me by their absence. This is based on the response of teachers, students, and my own occasional rereading of the book. 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.
To My Parents and to Uma, Umesh, Ajeet, Meera, and Maya or otherwise, without written permission from the Publisher Printed in the United Stares of America
mechanical, photocopying, microfilming, recording. 10013 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic. ISBN 0-8 01994, 1980 Plenum Press, New York A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. I n c l u d e s b i b l i o g r a p h i c a l r e f e r e n c e s and i n d e x. P r i n c i p l e s o f quantum mechanics / R. Library of Congress Cataloging-in-Publication Principles of Quantum Mechanics SECOND EDITION
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