Table Of Content

QUANTUM MECHANICS , INTERNATIONAL SERIES IN PURE AND APPLIED PHYSICS Leonard I. Schiff, Consulting Editor ADLER, BAZIN, and SCHIFFER Introduction to General Re.lativity ALLIS and HERLIN Thermodynamics and Statistical Mechanics BECKER Introduction to Theoretical Mechanics BJORKEN and DRELL Relativistic Quantum Fields BJORKEN and DRELL Relativistic Quantum Mechanics CHODOROW and SUSSKIND Fundamentals of Microwave Electronics CLARK Applied X-rays COLLI N Field Theory of Guided Waves EVANS The Atomic Nucleus FEYNMAN and HIBBS Quantum Mechanics and Path Integrals GINZTON Microwave Measurements HALL Introduction to Electron I'v\icroscopy HARDY and PERRIN The Principles of Optics HARNWELL Electricity and Electromagnetism HARNWELL and LIVINGOOD Experimental Atomic Physics HENLEY and THIRRING Elementary Quantum Field Theory HOUSTON Principles of Mathematical Physics JAMMER The Conceptual Development of Quantum Mechanics KENNARD Kinetic Theory of Gases LEIGHTON Principles of Modern Physics LINDSAY Mechanical Radiation LIVINGSTON and BLEWETT Particle Accelerators MIDDLETON An Introduction to Statistical Communication Theory MORSE Vibration and Sound MORSE and FESHBACH Methods of Theoretical Physics MORSE and INGARD Theoretical Acoustics MUSKAT Physical Principles of Oil Production NEWTON Scattering Theory of Waves and Particles PRESENT Kinetic Theory of Gases READ Dislocations in Crystals RICHTMYER, KENNARD, and LAURITSEN Introduction to Modern Physics SCHIFF Quantum Mechanics SCHWARTZ Introduction to Special Relativity SEITZ The Modern Theory of Solids SLATER Introduction to Chemical Physics SLATER Quantum Theory of Atomic Structure, VoL I SLATER Quantum Theory of Atomic Structure, Vol_ II SLATER Quantum Theory of Matter SLATER Electronic Structure of Molecules; Quantum Theory of Molecules and Solids, VoL 1 SLATER Symmetry and Energy Bands in Crystals: Quantum Theory of Molecules and . Solids, VoL 2 SLATER Insulators, Semiconductors, and Metals: Quantum Theory of Molecules and Solids, Vol. 3 SLATER and FRANK Introduction to Theoretical Physics SLATER and FRANK Mechanics _ SMYTHE Static and Dynamic Electricity STRATTON Electromagnetic Theory TINKHAM Group Theory and Quantum Mechanics TOWNES a~d SCHAWLOW Microwave Spectroscopy WANG SOlid-state Electronics WHITE Introduction to Atomic Spectra Thet~t~ ~iJ3~- R~chtmyer was Consulting Editor of the series from its inception in 1929 to his dea 1~47 to i954ee A_ Du Bridge was Consulting Editor from 1939 to 1946; and G. P_ Harnwell from . QUANTUM MECHANICS THIRD EDITION LEONARD I. SCHIFF Professor of Physics Stanford University McGRAW-Hill BOOK COMPANY New York St. Louis San Francisco Toronto London SYdney 530, I~ • QUANTUM MECHANICS Copyright © 1955, 1968 by McGraw-Hill, Inc. All Rights Reserved. Copyright 1949 by McGraw-Hill, Inc All Rights Reserved. Printed in the United States of America. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Library ofCongre88 Catalog Card Number 68-25665 .,)5287 3456n90 MAMM 7543210 TO FRANCES • PREFACE This volume has a threefold purpose: to explain the physical concepts of quantum mechanics, to describe the mathematical formalism, and to present illustrative examples of both the ideas and the methods. The book is intended to serve as a text at the graduate level and also as a reference book. It is assumed that the reader is reasonably familiar with classical mechanics, electromagnetic theory, atomic Rtructure, and dif ferential equations; prior acquaintance with matrices or group theory h" not necessary. In addition, he should have had some contact with com plex variables (for Chap. 9) and the special theory of relativity (for Chap. 13). The author believes that the analytical methods employed in the book will satiRfy most theoretical physicists even though no attempt is made to achieve mathematical rigor. For example, there is little or no discussion of the justification for the interchange of sum, derivative, and integral operations or for the use of the Ii function. On the other hand, the physical reasons for the nature of the results obtained are investigated wherever possible. Problems are given at the end of each chapter. They are often used to illustrate or amplify points discussed in the text. Original theoretical papers are referred to throughout the book; the list is representative rather than exhaustive. Experimental results are, for the most part, quoted without reference, since the large amount of documentation required for an adequate survey seems out of place in a book on theoretical physics. Several other books and review articles on quantum mechanics and related subjects are referred to for more detailed discussions of particular topics. • The scope of this volume is best outlined if the book is divided into \ ix