Quantum Mechanics In Nonlinear Systems

QUANTUM MECHANICS IN NONLINEAR SYSTEMS QUANTUM MECHANICS IN NONLINEAR SYSTEMS Pang Xiao-Feng University of Electronic Science and Technology of China, China Feng Yuan-Ping National University of Singapore, Singapore \[p World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONGKONG • TAIPEI • CHENNAI Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Co vent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Pang, Xiao-Feng, 1945Quantum mechanics in nonlinear systems / Pang Xiao-Feng, Feng Yuan-Ping, p. cm. Includes bibliographical references and index. ISBN 9812561161 (alk. paper) ISBN 9812562990 (pbk) 1. Nonlinear theories. 2. Quantum theory. I. Feng, Yuang-Ping. II. Title. QC20.7.N6P36 2005 530.15'5252-dc22 2004060119 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Copyright © 2005 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. Printed in Singapore by World Scientific Printers (S) Pte Ltd Preface This book discusses the properties of microscopic particles in nonlinear systems, principles of the nonlinear quantum mechanical theory, and its applications in condensed matter, polymers, and biological systems. It is intended for researchers, graduate students, and upper level undergraduate students. About the Book Some materials in the book are based on the lecture notes for a graduate course "Problems in nonlinear quantum theory" given by one of the authors (X. F. Pang) in his university in the 1980s, and a book entitled "Theory of Nonlinear Quantum Mechanics" (in Chinese) by the same author in 1994. However, the contents were completely rewritten in this English edition, and in the process, we incorporated recent results related to the nonlinear Schrodinger equations and the nonlinear Klein-Gordon equations based on research of the authors as well as other scientists in the field. The following topics are covered in 10 chapters in this book, the necessity for constructing a nonlinear quantum mechanical theory; the theoretical and experimental foundations on which the nonlinear quantum mechanical theory is based; the elementary principles and the theory of nonlinear quantum mechanics