Modern Physics And Quantum Mechanics

449 Pages·1971·34.473 MB·English

by  Elmer E. Anderson

MODERN
PHYSIOS
AND
QUANTUM
MEOHANIOS:
ELMER E. ANDERSON, Ph.D.
Chairman, D"port*ent of Physics,
Clnrkson College of Technobgy
Potsdarn, New York
. .
W. B. SAUNDERS COMPANY PHILADELPHIA LONDON TORONTO
1971
W. B. Saunders Company: West Washington Square
Philadelphia, Pa. 19105
l2 Dyott Street
London, WCIA lDB
1835 Yonge Street
Toronto 7. Ontario
Modern Physics and Quantum Mechanics sBN 0-7216-1220-2
e D7l by W. B. Saunders Company. Copyright under the International Copyright Union. All
rights reseived. This book is protected by copyright. No part of it may be reproduced, stored in a
relrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying,
recording. or otherwise, without written permission from the publisher. Made in the United States
of America. Press of W. B. Saunders Company. Library of Congress catalog card number
77-145554.
Print No.:
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This book grew out of my experience in teaching a one-year course in
quantum physics given to our seniors in the physics curriculum. It is designed
to bridge the gap between the descriptive course at the sophomore level and a
graduate course in quantum mechanics in which formai operator methods are
used freely. I have written this text because I have been unable to find a
book which suits our needs, although there ate a number of excellent texts
which are satisfactory for certain parts of the course.
Since many diverse areas ofmodern physics have developed simultaneously,
a strictly chronological presentation would not necessarily be the most logical
to follow. Therefore, I have chosen to develop the ideas that I consider
necessary for an understanding of quantum physics without regard to historical
order and with no attempt at complete coverage of all of twentieth century
physics. The use of the word "Modern" in the title is not intended to suggest
the same list of topics as is included in the sophomore course bearing that name.
It is assumed, in fact, that the student has previously taken such a course at
the sophomore level, as well as previous or concurrent courses in classical
mechanics, electromagnetic waves, and thermodynamics. Much of the material
of the first four chapters should not be new to the student but is included for
the sake of logical completeness in the development of quantum mechanics.
Four great conceptual edifices form the principal themes for the first
four chapters. These are: (l ) the special theory of relativity and some ex-
amples of its role in contemporary physics ; (2) the quantum theory of radiation
and the concept of the photon as a wave packet which can display both particle
and wave properties; (3) the Bohr theory of the atom and the quantization
of angular momentum; and (4) the representation of a particle by a wave
packet and the development of a wave mechanics for the description of a
particle's dynamical states. In Chapter 5, Schrddinger's wave mechanics is
applied to one-dimensional problems. In that chapter the linear harmonic
oscillator is solved by both the series and the operator methods in order to
familiarize the student with both of these approaches. This is followed in
Chapter 6 by a summary of the postulates of quantum mechanics and the
development of matrix mechanics. The angular momentum operators and
their eigenfunctions are introduced in Chapter 7 where they are applied to
ilt
tv PREFACE
the hvdrogen atom. The complexities resulting from spin and its interactions
u-ith orbital angular momenta are treated in Chapter B. The phenomenon
of exchange degeneracy resulting from the symmetry properties of identical
particles is also discussed in this chapter. Chapter 9 is an important chapter.
Here some approximate methods are introduced which enable the reader to
solrre large classes of real problems by means of the solutions obtained for the
ideal systems in earlier chapters. In Chapter 10, approximate methods are
applied to some specific atomic problems, and Chapter 11 is an introduction
to quantum mechanical scattering theory.
The book contains over 250 problems in addition to the numerical ex-
amples which are worked at appropriate points in the text. The importance
of solving a large number of problems in order to achieve a mastery of the
material cannot be overemphasized.
It is a pleasure to acknowledge the help of the following people and to
thank them for their indispensable roles in the preparation of this book: my
students over the past few years for their enthusiasm and inspiration; Agatha
Hollister and Amelia Anderson for typing and preparing the manuscript;
Rita Arajs for making all of the drawings; my colleagues, Professors Fred
Otter and Sigurds Arajs, as well as Professors Henri Amar of Temple University,
Paul H. Cutler of the Pennsylvania State University, Thomas B. W. Kirk of
Harvard University, John Reading of Northeastern University, John G.
Teasdale of San Diego State College, and an anonymous reviewer, for their
most valuable critical comments; to John J. Hanley and others of the staff
of the W. B. Saunders Co. for their assistance and encouragement; last of all,
to my mother and to my family-Amy, Kenneth, Mark, Scott, Ruth, and
Carl-to whom I dedicate this book.
Potsdam, Ir{ew York E. E. A.
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Sometimes the over-dramatization of the concepts of modern physics
tends to give the erroneous impression that success is achieved in the physical
sciences in proportion to one's rejection of what was previously regarded as
"intuitively obvious." The truth is, however, that the great natural philosophers
in the modern era have not rejected the obvious but have forced us to redefine
the obvious after taking a closer look at the evidence. The transition from
lgth to 20th century physics is replete with illustrations of redefinitions of such
concepts as space, time, causality, measurement, waves, particles, and so on.
Admittedly, there have been some bold postulates made by modern physicists,
but these generally arose out of the compelling urge either to incorporate new
experimental facts into known theory or to make existing theories consistent
with each other. It is hoped that the student of modern physics will learn to
appreciate its conceptual structure as well as its application to specific physical
problems.