Problems in Quantum Mechanics: With Solutions

268 Pages·1995·9.78 MB·English

by  Gordon Leslie Squires

Problem solving in physics is not simply a test of understanding
the subject, but is an integral part oflearning it. In this book, the
basic ideas and methods of quantum mechanics are illustrated by
means of a carefully chosen set of problems, complete with
detailed, step-by-step solutions. .
After a preliminary chapter on orders of magnitude, a variety
of topics are covered, including the postulates of quantum
mechanics, Schrodinger's equation, angular momentum, the
hydrogen atom, the harmonic oscillator, spin, time-independent
and time-dependent perturbation theory, the variational method,
identical particles, multielectron atoms, transitions and scatter
ing. Most of the chapters start with a summary of the relevant
theory, outlining the required background for a given group of
problems. Considerable emphasis is placed on examples from
atomic, solid-state and nuclear physics, particularly in the latter
partof the book as the student's familiarity with the concepts and
techniques increases. .
Throughout, the physical interpretation or application of the
results is highlighted, thereby providing useful insights into a
wide range of systems and phenomena. This approach will make
the book invaluable to anyone taking an undergraduate course in
quantum mechanics.

Problems in quantum mechanics
with solutions

Problems in
quantum mechanics
with solutions
G. L. SQUIRES
.Emeritus Lecturer in Physics at the University ofCambridge
and Fellow ofTrinity College, Cambridge
gCAMBRIDGE
V
UNIVERSITY PRESS
PUBLISHED BY TIBI IJIUIIHI NYNI)ICA'rn Olf TI-I11 UNIVI:llUII'I'Y Olt CAMIHU)OIl
The Pitt Building, Trurnplngton Street, Cambridge, United Kingdom
CAMBRIDGE UNIVERSITY PRESS
The Edinburgh Building, Cambridge CB2 2RU, UK
40 West 20th Street, New York,NY 10011-4211, USA
477 Williamstown Road, Port Melbourne, VIC 3207, Australia
Ruiz deAlarcon 13, 28014 Madrid, Spain
Dock House, The Waterfront, Cape Town 8001, South Africa
http:/www.cambridge.org
© Cambridge University Press 1995
This book is incopyright. Subjectto statutory exception
and to the provisions ofrelevantcollective licensing agreements,
noreproduction ofany partmay take place without
the written permission ofCambridge University Press.
First published 1995
Reprinted 1995, 1996,2002
Typeset in LinotronTimes 10/12.5 pt
A catalogue recordfor this bookis available.from the British Library
Library ofCongress Cataloguing in Publication Data
Squires, G~ L. (Gordon Leslie)
Problems in quantum mechanics with solutions / G. L. Squires.
p. em.
Includes bibliographicalreferences and index.
ISBN 0-521-37245-3. - ISBN 0-521-37850-8 (pbk.)
1. Quantum theory- Problems, exercises, etc. L Title,
QC174. 15.8661995
530. 1'2 - dc20 93-43931 elP
ISBN 0 521 37245 3 hardback
ISBN 0 521 378508 paperback
Transferredto digital printing2003
KT
Contents
Acknowledgements Vlll
Preface [or the reader ix
1 Numericalvalues 1
Values of physicalconstants 1 . Problems 2 Solutions 4
2 Fundamentals 9
Summary of theory 9 Problems 14 Solutions 17
3 .Sehrddinger equation 30
Summary of theory 30 Problems 32 Solutions 36
4 Orbitalangularmomentum, hydrogen atom, harmonic
oscillator 51
Summary of theory 51 Problems 55 Solutions 58
5 Matrices, spin, addition of angular momentum 74
Summary of theory 74 Problems '82 Solutions 87
6 Approximationmethods. 109
Time-independentperturbationtheory, variationalmethod
Summary of theory 109 Problems 112 Solutions 114
7 Identical particles, multielectron atoms 128
Summary of theory 128 Problems 133 Solutions 136
8 Time, time-dependentperturbatlen theory, transitions 155
Summary of theory 155 Problems 158 Solutions 162
9 Scattering, reactions 179
Summary of theory 179 Problems 185 Solutions 189
10 Miscellaneous 207
Problems 207 Solutions 215
References 250
Index 251
vii
Acknowledgements
I started this book in 1969. I took sabbatical leave in 1970,at the Hebrew
University in Jerusalem, intending to finish it there. However I was
side-tracked by meeting the woman whom I subsequently married. So,
like P. G. Wodehouse, I dedicate this book to my wife, but for whom it
would have been written twenty three years ago.
I wishto thank Dr K. F. Riley, and MessrsS. R. Johnson, S. Patel, and
B. E. Rafferty who read parts of the manuscript and made several useful
comments on it, 1 am. particularly grateful to Dr M. E. Cates and Messrs
D. M. Freye, F. M.Grosche, R. K. W. Haselwimmer, R. J. F. Hughes;
and C. S. Reynolds, who between them worked through the problems
and made valuable comments and suggestions. Finally, I wish to
acknowledge my indebtedness to all the undergraduates, mainly from
Trinity College, whom I have supervised in Quantum Mechanics in the
last thirty years. In the words of the proverb 'I have learnt much from my
teachers, but more from. mypupils.'
G. L. Squires