Principles of quantum mechanics as applied to chemistry and chemical physics 1999 - Fitts(1).pdf

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PRINCIPLES OF
QUANTUM
MECHANICS:
as Applied to Chemistry
and Chemical Physics
DONALD D. FITTS
CAMBRIDGE UNIVERSITY PRESS
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PRINCIPLES OF QUANTUM MECHANICS
as Applied to Chemistry and Chemical Physics
This text presents a rigorous mathematical account of the principles of
quantum mechanics, in particular as applied to chemistry and chemical
physics. Applications are used as illustrations of the basic theory.
The ®rst two chapters serve as an introduction to quantum theory, although it
is assumed that the reader has been exposed to elementary quantum mechanics
as part of an undergraduate physical chemistry or atomic physics course.
Following a discussion of wave motion leading to SchrÈ dinger's wave mech-
anics, the postulates of quantum mechanics are presented along with the
essential mathematical concepts and techniques. The postulates are rigorously
applied to the harmonic oscillator, angular momentum, the hydrogen atom, the
variation method, perturbation theory, and nuclear motion. Modern theoretical
concepts such as hermitian operators, Hilbert space, Dirac notation, and ladder
operators are introduced and used throughout.
This advanced text is appropriate for beginning graduate students in chem-
istry, chemical physics, molecular physics, and materials science.
A native of the state of New Hampshire, Donald Fitts developed an interest in
chemistry at the age of eleven. He was awarded an A.B. degree, magna cum
laude with highest honors in chemistry, in 1954 from Harvard University and a
Ph.D. degree in chemistry in 1957 from Yale University for his theoretical work
with John G. Kirkwood. After one-year appointments as a National Science
Foundation Postdoctoral Fellow at the Institute for Theoretical Physics, Uni-
versity of Amsterdam, and as a Research Fellow at Yale's Chemistry Depart-
ment, he joined the faculty of the University of Pennsylvania, rising to the rank
of Professor of Chemistry.
In Penn's School of Arts and Sciences, Professor Fitts also served as Acting
Dean for one year and as Associate Dean and Director of the Graduate Division
for ®fteen years. His sabbatical leaves were spent in Britain as a NATO Senior
Science Fellow at Imperial College, London, as an Academic Visitor in
Physical Chemistry, University of Oxford, and as a Visiting Fellow at Corpus
Christi College, Cambridge.
He is the author of two other books, Nonequilibrium Thermodynamics
(1962) and Vector Analysis in Chemistry (1974), and has published research
articles on the theory of optical rotation, statistical mechanical theory of
transport processes, nonequilibrium thermodynamics, molecular quantum
mechanics, theory of liquids, intermolecular forces, and surface phenomena.
PRINCIPLES OF
QUANTUM MECHANICS
as Applied to Chemistry and Chemical Physics
DONALD D. FITTS
University of Pennsylvania
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PUBLISHED BY CAMBRIDGE UNIVERSITY PRESS (VIRTUAL PUBLISHING)
FOR AND ON BEHALF OF THE PRESS SYNDICATE OF THE UNIVERSITY OF
CAMBRIDGE
The Pitt Building, Trumpington Street, Cambridge CB2 IRP
40 West 20th Street, New York, NY 10011-4211, USA
477 Williamstown Road, Port Melbourne, VIC 3207, Australia
http://www.cambridge.org
© D. D. Fitts 1999
This edition © D. D. Fitts 2002
First published in printed format 1999
A catalogue record for the original printed book is available
from the British Library and from the Library of Congress
Original ISBN 0 521 65124 7 hardback
Original ISBN 0 521 65841 1 paperback
ISBN 0 511 00763 9 virtual (netLibrary Edition)
Contents
Preface
viii
Chapter 1 The wave function
1
1.1 Wave motion
2
1.2 Wave packet
8
1.3 Dispersion of a wave packet
15
1.4 Particles and waves
18
1.5 Heisenberg uncertainty principle
21
1.6 Young's double-slit experiment
23
1.7 Stern± Gerlach experiment
26
1.8 Physical interpretation of the wave function
29
Problems
34
Chapter 2 SchrÈ dinger wave mechanics
36
2.1 The SchrÈ dinger equation
36
2.2 The wave function
37
2.3 Expectation values of dynamical quantities
41
2.4 Time-independent SchrÈdinger equation
46
2.5 Particle in a one-dimensional box
48
2.6 Tunneling
53
2.7 Particles in three dimensions
57
2.8 Particle in a three-dimensional box
61
Problems
64
Chapter 3 General principles of quantum theory
65
3.1 Linear operators
65
3.2 Eigenfunctions and eigenvalues
67
3.3 Hermitian operators
69
v

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