Table Of Content
Crude Values of Important Physical Constants
The constants in this table might well be memorized so that
they are always available for simple estimates. See Table A
in Appendix for precise values.
Avogadro's number: No = 6 X 1023 (mol)-1
Velocity of light: c = 3 x 1010 cm/sec
Electronic charge: e = 1.6 x 10-1 coulomb
Fine-structure constant: a = 1/137
Rest energy of electron: mc? = 0.5 MeV
Rest energy of proton: M,c? = 940 MeV
Ratio of proton to electron mass: M,/m ~ 1800
lonization energy of hydrogen: R., = }a2mc? = 13.6 eV
Bohr radius in hydrogen: ay = X/a = 0.5 A = 0.5 x 10-8 cm
Bohr magneton: (eti)/(2mc) = 5.8 x 10-9 eV/gauss
Nuclear radius (mass number A): r ~ Al/3 x (1.2 x 10-13 em)
Nuclear binding energy/nucleon: ~ 8 MeV
“Room temperature’: k x (293°K) = (1/40) eV
“Optical region”: 4000 A-7000 A
3.0 eV-1.8 eV
ONE ELECTRON VOLT corresponds to:
Temperature: = 12,000°K
Frequency: = 2.4 x 1014 cycles/sec
Bulk energy: = 23,000 cal/mol
Wave number: ~ 8000 cm-1
Wavelength: = 12,000 A
Front cover: Term scheme of neutral thallium atom.
Back cover: Baryon decuplet.
quantum
physics
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quantum
physics
berkeley physics course—volume 4
Eyvind H. Wichmann
Professor of Physics
University of California, Berkeley
~ 7 JUIN 197 1
The preparation of this course was supported by a grant
from the National Science Foundation to Education
Development Center, Incorporated,
Cm 20407, )
fi
Loe alia J CrmPorans
\anqu are AGso4 - 39
QUANTUM PHYSICS
Copyright © 1967, 1971 by Education Develop-
ment Center, Inc. (successor by merger to
Educational Services Incorporated), All rights
reserved. Printed in the United States of
America: This book, or parts thereof, may not
be reproduced in any form without the written
permission of Education Development Center,
Inc., Newtor, Massachusetis.
LAbrary of Congress Catalog Card Number
64-66016
04861
1234567890 MWMW 79876543210
Preface to the Berkeley Physics Course
This is a two-year introductory college physics course for students
majoring in science and engineering. The intention of the writers
has been to present physics in so far as possible as it appears to
physicists working on the forefront of their field. We have sought
to make a course which would vigorously emphasize the foundations
of physics. Our specific objectives were to introduce students early
to the ideas of special relativity, of quantum physics, and of statis-
tical physics. At the same time we wanted our presentation to be
of an elementary character, and it was never our intention to de-
velop a course limited to honors students or to students in advanced
standing. This course is intended for any student who has had
physics in high school. A mathematics course including calculus
should be taken concurrently,
The five volumes of the course include:*
I. Mechanics (Kittel, Knight, Ruderman)
H. Electricity and Magnetism (Purcell)
II. Waves (Crawford)
IV. Quantum Physics (Wichmann)
V. Statistical Physics (Reif)
The initial work on this course led Alan M. Portis to devise a new
elementary physics laboratory, now known as the Berkeley Physics
Laboratory. Because the course emphasizes the principles of
physics, some teachers may feel that it does not deal sufficiently
with experimental physics. The laboratory is rich in important ex-
periments, and is designed to balance the whole course.
In recent years several new college physics courses have been
planned and developed in the United States. The idea of making a
new course has come to many physicists, aware of developments in
science and engineering, and of the increasing emphasis on science
in elementary schools and in high schools. Our own course was
conceived in a conversation between Philip Morrison, now of the
* OF these Volumes I, TI, III, and V have appeared previously. The changes in our
common preface for the present volume reffect some organizational changes under
which this volume was prepared.
vo
vi Preface to the Berkeley Physics Course
Massachusetts Institute of Technology, and C. Kittel late in 1961.
We were encouraged by John Mays and his colleagues of the Na-
tional Science Foundation and by Walter C. Michels, then the
Chairman of the Commission on College Physics. An informal
committee was formed under the Chairmanship of C. Kittel to
guide the course through the initial stages. The committee met first
in May 1962, in Berkeley, and at that time drew up a tentative out-
line, incorporating topics and attitudes which we believed should
and could be taught to beginning college students of science and
engineering. The membership of the committee has since under-
gone some changes, and it now consists of the undersigned. In the
development of the course each author has been free to choose that
style and methed of presentation which seemed to him appropriate
to his subject.
The financial support of the course development was provided by
the National Science Foundation, with considerable indirect sup-
port by the University of California. The funds were administered
by Education Development Center, Incorporated* (EDC), a non-
profit organization established to administer curriculum improve-
ment programs. We are particularly indebted to Gilbert Oakley,
James Aldrich, and William Jones, all of EDC, for their sympathetic
and vigorous support. EDC established an office in Berkeley, most
recently under the very competent direction of Mrs. Lila Lowell, to
assist the development of the course and the laboratory.
The University of California has had no official connection with
our program, but it has aided us in important ways. For this help
we thank Professor Burton J. Moyer, Chairman of the Department
of Physics, and the faculty and nonacademic staff of the Depart-
ment. We are particularly grateful to those of our colleagues who
have tried this course in the classroom and who, on the basis of their
experience, have offered criticism and suggestions for improve-
ments,
Your corrections and suggestions will always be welcome.
Frank S. Crawford, Jr.
Charles Kittel
Walter D. Knight
Alan M. Portis
Frederick Reif
Malvin A. Ruderman
Eyvind H. Wichmann
A. Carl Helmholz
Edward M. Purcell } Chairmen
* Formerly Educational Services Incorporated.
Preface to Volume IV
This volume of the Berkeley Physics Course is devoted to Quantum
Physics. It is an introductory book, intended for the student whose
background in physics corresponds to a fair fraction of the material
in the preceding volumes of the series. My ideal reader-leamer is
thus a student of science or engineering in his sophomore year. To
postpone the study of all aspects of quantum phenomena beyond
the sophomore level does not seem reasonable and fair today in
view of the developments in physics during the last fifty years. A
well-balanced introductory course should certainly reflect some of
these developments.
Ido not believe that the study of quantum physics is intrinsically
more difficult than the study of any other branch of physics. In
every domain of physics we encounter phenomena which we feel
are simple and transparent, as well as phenomena which are very
difficult to account for in a quantitative fashion. It is true, of
course, that all quantum phenomena were at one time regarded as
highly mysterious and perplexing. In the period during which the
field was first explored, physicists experienced very real psycholog-
ical difficulties which derived partly from understandable prejudices
in favor of the classical view of the world, and partly from the frag-
mentary nature of the experimental picture. There is, however, no
reason why these same difficulties have to be re-created for the
beginning student of today. It is now known with certainty that
the classical description is only approximately correct, and there is
now available an enormous body of experimental results which sup-
port and illuminate various aspects of present theoretical ideas. 1
firmly believe that among the known facts one can find topics for
discussion which are clear-cut and simple enough to be dealt with
in an elementary manner, but which at the same time illuminate
important ideas and principles. I doubt very much that the student
who is guided to think about a well-chosen sequence of simple but
significant physical facts will feel that quantum phenomena are
more mysterious than, say, the phenomenon of universal gravitation.
My purpose in this book is to present characteristic examples of
quantum phenomena, to acquaint the reader with typical orders of
ott
viii Preface to Volume IV
magnitude of physical parameters in microphysics, and to introduce
him to quantum-mechanical thinking. I have tried to include
among my topics for discussion, phenomena and issues which are of
particular importance for the understanding of physics. At the
same time I have tried to keep the discussion as elementary as pos-
sible. Ihave selected my topics from the various domains of micro-
physics, but I have made no attempt to present a detailed systematic
account of any of these domains. Such accounts should, in my
opinion, be left for courses at the junior-senior level.
The requirements with respect to mathematical preparation are
modest. I assume that the reader has had a course in calculus, in-
cluding a first introduction to ordinary differential equations and
some vector analysis. In order to prevent a shift of attention from
the physical issues to technical mathematical questions, I have tried
to avoid topics which at this stage might appear mathematically
difficult. Topics which call for some knowledge of the properties
of special functions, or of the method of separation of variables in
the theory of partial differential equations, are not discussed at all,
With regard to algebra I have concluded, with some regrets, that I
should not assume familiarity with matrix theory, and I have there-
fore avoided topics for which matrix theory is the natural mathe-
matical tool.
1 do not by any means believe that the fulfillment of the general
aims of this part of the course demands that all the material in this
book be taught in class. On the contrary I wanted to leave the in-
structor considerable latitude in the selection of topics for discus-
sion. To aid the instructor in the planning of his course I discuss the
specific aims of the various chapters in the teaching notes following
this preface, and I try to outline what might be regarded as a min-
imum program. I feel there is no harm in having more material
available for reading than is actually taught in class, as there will
always be some students who will want to read beyond the lectures.
Eyvind H. Wichmann
October, 1967
Berkeley, California
