com Useful Constants and Conversion Factors Quoted to a useful number of significant figures. Speed of light in vacuum c = 2.998 x 108 m/sec Electron charge magnitude e = 1.602 x 1 0 = 19 coul Planck's constant h = 6.6582 x 10 -15 eV-sec Boltzmann's constant k = 1.617 x 10 -5 eV/ °K Avogadro's number No = 6.023 x 1023/mole Coulomb's law constant 1 /47rE0 = 8.988 x 109 nt - m2 /coul2 Electron rest mass me = 9.5110 MeV/c 2 Proton rest mass p = 1.3 MeV/c2 m Neutron rest mass m„ = 1.6 MeV/c 2 Atomic mass unit (C 12 = 12) -27 kg = 931.6x0 Bohr magneton ub = eh/2me = 9.27 x 10 -24 amp-m2 (or joule/tesla) Nuclear magneton µn = eh/2m, = 5.05 x 10 -27 amp-m2 (or joule /tesla) Bohr radius ao = 47c€0h2/mee2 = 5.529 A Bohr energy E1 = — mee 4/(4rcE0)22h2 = —2.6 eV Electron Compton wavelength Ac = h/mec = 2.0243 A Fine-structure constant a = e2 /4nE 0hc = 7.30 x 10 -3 1/137 kT at room temperature k300 °K = 0.0258 eV ^ 1/40 eV 1eV= 1.242 x 10 18 eV 1 A=10 -10 m 1F=10 -15 m l barn (bn)= 10-28m2 www.com QUANTUM PHYSICS www.com Assisted by yid O CaIgweal Univer^^#y^qf^#^rni^ ^^ arbara United'•°Stalês C^^t^^ ^,;^^ Odemy The figure on the cover is frori ; èction 9-4, where it is used to show the tendency „ for two identical spin 1/2 particles (such as electrons) to avoid each other if their spins are essentially parallel. This tendency, or its inverse for the antiparallel case, is one of the recurring themes in quantum physics explanations of the properties of atoms, molecules, solids, nuclei, and particles.com QUANTUM PHYSICS of Atoms, Molecules, Solids, Nuclei, and Particles Second Edition ROBERT EISBERG University of California, Santa Barbara JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore www.com Copyright © 1974, 1985, by John Wiley & Sons, Inc. All rights reserved.
Published simultaneously in Canada. Reproduction or translation of any part of this work beyond that permitted by Sections 107 and 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department, John Wiley & Sons. Library of Congress Cataloging in Publication Data: Eisberg, Robert Martin.
Quantum physics of atoms, molecules, solids, nuclei, and particles. Resnick, Robert, 1923— II.1'2 84-10444 ISBN 0-471-87373-X Printed in the United States of America Printed an d bound by the Hamilton Printing Comp any.com PREFACE TO THE SECOND EDITION The many developments that have occurred in the physics of quantum systems since the publication of the first edition of this book—particularly in the field of elementary particles—have made apparent the need for a second edition. In preparing it, we solicited suggestions from the instructors that we knew to be using the book in their courses (and also from some that we knew were not, in order to determine their objections to the book). The wide acceptance of the first edition made it possible for us to obtain a broad sampling of thought concerning ways to make the second edition more useful.
We were not able to act on all the suggestions that were re- ceived, because some were in conflict with others or were impossible to carry out for technical reasons. But we certainly did respond to the general consensus of these suggestions. Many users of the first edition felt that new topics, typically more sophisticated aspects of quantum mechanics such as perturbation theory, should be added to the book. Yet others said that the level of the first edition was well suited to the course they teach and that it should not be changed.
We decided to try to satisfy both groups by adding material to the new edition in the form of new appendices, but to do it in such a way as to maintain the decoupling of the appendices and the text that characterized the original edition. The more advanced appendices are well inte- grated in the text but it is a one-way, not two-way, integration. A student reading one of these appendices will find numerous references to places in the text where the development is motivated and where its results are used. On the other hand, a student who does not read the appendix because he is in a lower level course will not be frustrated by many references in the text to material contained in an appendix he does not use.
Instead, he will find only one or two brief parenthetical statements in the text advising him of the existence of an optional appendix that has a bearing on the subject dealt with in the text. The appendices in the second edition that are new or are significantly changed are: Appendix A, The Special Theory of Relativity (a number of worked-out examples added and an important calculation simplified); Appendix D, Fourier Integral De- scription of a Wave Group (new); Appendix G, Numerical Solution of the Time- Independent Schroedinger Equation for a Square Well Potential (completely rewritten to include a universal program in BASIC for solving second-order differential equa- tions on microcomputers); Appendix J, Time-Independent Perturbation Theory (new); Appendix K, Time-Dependent Perturbation Theory (new); Appendix L, The Born Approximation (new); Appendix N, Series Solutions of the Angular and Radial Equations for a One-Electron Atom (new); Appendix Q, Crystallography (new); Appendix R, Gauge Invariance in Classical and Quantum Mechanical Electromag- netism (new). Problem sets have been added to the ends of many of the appendices, both old and new. In particular, Appendix A now contains a brief but comprehensive set of problems for use by instructors who begin their "modern physics" course with a treatment of relativity.com A large number of small changes and additions have been made to the text to improve and update it.
There are also several quite substantial pieces of new mate- PREFA CE TO THE S ECO ND EDITIO N rial, including: the new Section 13-8 on electron-positron annihilation in solids; the additions to Section 16-6 on the Mössbauer effect; the extensive modernization of the last half of the introduction to elementary particles in Chapter 17; and the en- tirely new Chapter 18 treating the developments that have occurred in particle phy- sics since the first edition was written. We were very fortunate to have secured the services of Professor David Caldwell of the University of California, Santa Barbara, to write the new material in Chapters 17 and 18, as well as Appendix R. Only a person who has been totally immersed in research in particle physics could have done what had to be done to produce a brief but understandable treatment of what has happened in that field in recent years. Furthermore, since Caldwell is a colleague of the senior author, it was easy to have the interaction required to be sure that this new material was closely integrated into the earlier parts of the book, both in style and in content.
Prepublication reviews have made it clear that Caldwell's material is a very strong addition to the book. Professor Richard Christman, of the U. Coast Guard Academy, wrote the new material in Section 13-8, Section 16-6, and Appendix Q, receiving significant input from the authors. We are very pleased with the results.
The answers to selected problems, found in Appendix S, were prepared by Profes- sor Edward Derringh, of the Wentworth Institute of Technology. He also edited the new additions to the problem sets and prepared a manual giving detailed solutions to most of the problems. The solutions manual is available to instructors from the publisher. It is a pleasure to express our deep appreciation to the people mentioned above.
We also thank Frank T. Avignone, III, University of South Carolina; Edward Cecil, Colorado School of Mines; L. Edward Millet, California State University, Chico; and James T. Tough, The Ohio State University, for their very useful prepublication reviews.
The following people offered suggestions or comments which helped in the develop- ment of the second edition: Alan H. Barrett, Massachusetts Institute of Technology; Richard H. Behrman, Swarthmore College; George F. Bertsch, Michigan State Uni- versity; Richard N.
Boyd, The Ohio State University; Philip A. Casabella, Rensselaer Polytechnic Institute; C. Dewey Cooper, University of Georgia; James E. Draper, University of California at Davis; Arnold Engler, Carnegie-Mellon University; A., Auburn University; Ross Garrett, University of Auckland; Russell Hobbie, University of Minnesota; Bei-Lok Hu, University of Maryland; Hillard Hun- tington, Rensselaer Polytechnic Institute; Mario Iona, University of Denver; Ronald G.
Johnson, Trent University; A. Laskar, Clemson University; Charles W. Leming, Henderson State University; Luc Leplae, University of Wisconsin-Milwaukee; Ralph D. Meeker, Illinois Benedictine College; Roger N.
Metz, Colby College; Ichiro Miya- gawa, University of Alabama; J. Moore, Brock University; John J. O'Dwyer, State University of New York at Oswego; Douglas M. Potter, Rutgers State University; Russell A.
Schaffer, Lehigh University; John W. Watson, Kent State University; and Robert White, University of Auckland. We appreciate their contribution. Santa Barbara, California Robert Eisberg Troy, New York Robert Resnick www.com PREFACE TO THE FIRST EDITION The basic purpose of this book is to present clear and valid treatments of the prop- erties of almost all of the important quantum systems from the point of view of elementary quantum mechanics.
Only as much quantum mechanics is developed as is required to accomplish the purpose. Thus we have chosen to emphasize the applica- tions of the theory more than the theory itself. In so doing we hope that the book will be well adapted to the attitudes of contemporary students in a terminal course on the phenomena of quantum physics. As students obtain an insight into the tre- mendous explanatory power of quantum mechanics, they should be motivated to learn more about the theory.
Hence we hope that the book will be equally well adapted to a course that is to be followed by a more advanced course in formal quantum mechanics. The book is intended primarily to be used in a one year course for students who have been through substantial treatments of elementary differential and integral cal- culus and of calculus level elementary classical physics. But it can also be used in shorter courses. Chapters 1 through 4 introduce the various phenomena of early quantum physics and develop the essential ideas of the old quantum theory.
These chapters can be gone through fairly rapidly, particularly for students who have had some prior exposure to quantum physics. The basic core of quantum mechanics, and its application to one- and two-electron atoms, is contained in Chapters 5 through 8 and the first four sections of Chapter 9. This core can be covered well in appre- ciably less than half a year. Thus the instructor can construct a variety of shorter courses by adding to the core material from the chapters covering the essentially independent topics: multielectron atoms and molecules, quantum statistics and solids, nuclei and particles.
Instructors who require a similar but more extensive and higher level treatment of quantum mechanics, and who can accept a much more restricted coverage of the applications of the theory, may want to use Fundamentals of Modern Physics by Robert Eisberg (John Wiley & Sons, 1961), instead of this book. For instructors requir- ing a more comprehensive treatment of special relativity than is given in Appendix A, but similar in level and pedagogic style to this book, we recommend using in addition Introduction to Special Relativity by Robert Resnick (John Wiley & Sons, 1968). Successive preliminary editions of this book were developed by us through a pro- cedure involving intensive classroom testing in our home institutions and four other schools. Robert Eisberg then completed the writing by significantly revising and extending the last preliminary edition.
He is consequently the senior author of this book.