Problems and Solutions in Quantum Chemistry and Physics

685 Pages·2013·20.7 MB·English

by  Johnson

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To
Ellen and Barbara
Copyright © 1986 by Charles S. Johnson, Jr., and Lee G. Pedersen.
All rights reserved under Pan American and International Copyright
Conventions.

This Dover edition, first published in 1986, Is an unabridged and further
corrected verson of the corrected third printing of the work originally published
in 1974 by Addison-Wesley Publishing Company, Inc., Reading, Massachusetts.

Library of Congress Cataloging-in-Publicatlon Data Johnson, Charles S.
(Charles Sidney), 1936– Problems and solutions in quantum chemistry and
physics.
Reprint. Originally published: Reading, Mass.: Addison-Wesley Pub. Co., 1974.
Bibliography: p.
Includes index.
1. Quantum chemistry—Problems, exercises, etc. 2. Quantum theory—
Problems, exercises, etc. I. Pedersen, Lee G. II. Title.
QD462.J63 1986 540.2’8’076 86-16820
9780486151533

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FOREWORD
We have prepared this book of problems to aid students and teachers of quantum
chemistry and physics. The level of the material is similar to that found in
advanced physical chemistry and introductory quantum mechanics courses. In
developing this book we have been guided by our belief that an exposition of the
principles of quantum theory is often not sufficient for the beginning student,
and that numerous examples, illustrations, and exercises can be an aid to
understanding and to the development of the proper kind of intuition. Education
in this subtle field must be to a large extent self education.
We believe that this collection is unique in the variety of problems covered
and in the detail with which the solutions are presented. There is a wider range
of applications in each chapter than can be found in most standard quantum
chemistry texts. Each chapter includes a brief introduction followed by about
twenty problems of increasing difficulty for which detailed solutions are
provided. These are followed in each chapter by a section of “supplementary”
problems, which have answers but not solutions. Ten appendices on
mathematical topics have been included for the convenience of the reader. We
have attempted to maintain a continuity in each chapter so that the logical
development of concepts and techniques can be followed.
For completeness a number of standard topics, e.g. the quantum treatment of
the harmonic oscillator, have been presented in the problem-and-answer format.
Also included are many of the more or less standard problems, which have
appeared in textbooks and in problem collections. We have encountered or
developed many of the problems in this collection in the course of teaching
advanced physical chemistry, spectroscopy, and quantum chemistry. The
American Journal of Physics and the Journal of Chemical Education have been
important sources. We have not attempted to itemize all of the problem sources,
but have made an effort to refer to useful discussions in the literature. The
reference list is, of course, biased somewhat toward those texts which we happen
to own.
It is certain that some errors have slipped in as we have modified and recopied
old problems, constructed new problems, and converted many solutions to SI
old problems, constructed new problems, and converted many solutions to SI
units. Conceptual errors may, of course, also be present. We plan to maintain a
list of errors, and would appreciate receiving communications concerning
suspected errors from readers. We apologize for the errors and for the omission
of some important topics. Perhaps the deficiencies can be remedied in a later
edition.
We have benefited considerably from discussions with our colleagues, and
from courses taught in chemistry and physics at the University of North
Carolina. Professors A. D. Buckingham (Cambridge University), S. H. Lin
(Arizona State University), and J. L. Whitten (SUNY at Stony Brook) kindly
read parts of the manuscript and made useful suggestions. All of the remaining
errors are, of course, ours. Part of the manuscript: was written at Cambridge
where one of us (C.S.J.) was a Guggenheim Fellow (1972–973).
We wish especially to thank Mrs. Becky Smith for her patient typing of
several versions of the manuscript. Without her diligence and accuracy the book
would have been greatly delayed.
Finally we thank our wives, Ellen and Barbara, for their encouragement and
patience during the last three years.

Chapel Hill 1973
Charles S. Johnson, Jr.
Lee G. Pedersen

In this second printing we have taken the opportunity to correct a number of
errors. We would like to thank our colleagues at North Carolina and elsewhere
for pointing out these errors and inconsistencies. Special thanks are in order for
Professor E. Merzbacher (University of North Carolina) who made numerous
suggestions. Again we encourage readers to inform us of suspected errors.

Chapel Hill 1976
Charles S. Johnson, Jr.
Lee G. Pedersen