Download topics in atomic physics - University of Missouri

TOPICS IN ATOMIC PHYSICS
C. E. Burkhardt
Department of Physics
St. Louis Community College
St. Louis, MO 63135
&
J. J. Leventhal
Department of Physics
University of Missouri - St. Louis
St. Louis, MO 63121
PREFACE
Our intention in writing this book was to provide a foundation for students to begin
research in modern atomic physics. Of course, any specialized textbook necessarily
reflects the predilection of the authors toward certain aspects of the subject. This one is
no exception. It reflects our belief that a thorough understanding of the unique properties
of the hydrogen atom is essential to an understanding of atomic physics. It also reflects
our fascination with the distinguished position that Mother Nature has bestowed on the
pure Coulomb and Newtonian potentials, and thus hydrogen atoms and Keplerian orbits.
We have therefore devoted a large portion of this book to the hydrogen atom in order to
emphasize this distinctiveness. We attempt to stress the uniqueness of the attractive 1/r
potential without delving into group theory. It is our belief that, once an understanding of
the hydrogen atom is achieved, the properties of multi-electron atoms can be understood
as departures from hydrogenic properties.
From the beginning, it was our intention to include information in this book that is not
easily located elsewhere. To this end we have incorporated derivations that are difficult to
find in other books and, indeed, even in the literature. For example, the quantum
mechanical Lenz vector operator is not often discussed in quantum mechanics and atomic
physics books. When it is discussed, it is usually stated that it commutes with the
hydrogen atom Hamiltonian, but it is difficult to find this proven. We give this proof in
some detail. In fact, one of the general features of our book is that often we include more
algebraic steps than are traditionally given in textbooks. Our reasoning is that we wish to
relieve the reader of the task of reproducing algebra and thus permit concentration on the
physics.
The material is intended to be suitable for a one semester graduate or advanced
undergraduate level course in Atomic Physics. It is assumed that the student has had at
least introductory quantum mechanics, although pertinent topics such as perturbation
theory and variational techniques are briefly reviewed. Chapter 1 presents some
background material which, in large part, is review. In this chapter the utility of the Bohr
atom is discussed and the derivation performed as Bohr did it. This is in contrast to most
modern presentations. Chapters 2 and 3 are standard reviews of angular momentum
algebra with emphasis on aspects pertinent to atomic physics. Chapter 4 is a discussion of
the quantum mechanical hydrogen atom and the separation of the Schrödinger equation in
both spherical and parabolic coordinates. Emphasis is placed on the conditions that force
quantization. Also included in this chapter is an attempt to clarify the difference between
two commonly used definitions of both Laguerre and associated Laguerre polynomials.
In most treatments of the quantum mechanical hydrogen no mention is made of alternate
definitions. Chapter 5 is a discussion of the classical hydrogen atom. Naturally it draws
heavily on Keplerian orbits and the consequences of the additional constant of the
classical motion, the Lenz vector. Chapter 6 is a lengthy discussion of the accidental
degeneracy of the hydrogen atom and its causes in the context of the quantum mechanical
analog of the Lenz vector. To our knowledge, the material in Chapters 6 and 7 are not
covered in any modern text. In Chapter 8 we discuss the breaking of the accidental
degeneracy via fine structure, the Lamb shift and hyperfine structure. The treatment is
fairly standard. In Chapter 8 we treat the hydrogen atom in external fields. The
description of the Zeeman effect is standard, but the weak field Stark effect is described
both quantum mechanically and classically. Of course, the classical treatment leans
heavily on the results of Chapter 5.
SI units are used except in those instances for which we believe that atomic units are
considerably more convenient. For instance, the Zeeman effect is treated using SI units
because the Bohr magneton times the magnetic induction field provides a convenient
measure of the Zeeman energy. On the other hand, we find atomic units to be more
convenient in the treatment of the Stark effect. Chapters 9 and 10 are discussions of
multi-electron atoms, beginning with helium in Chapter 9. The presentation is quite
standard. Chapter 11 presents the quantum defect in a way that is seldom seen in texts. In
keeping with the theme of this book the quantum defect is related to classical concepts
and the correspondence principle. Chapter 12 deals with multi-electron atoms in external
fields. Here again the Zeeman effect is treated in the standard manner, but the Stark effect
is presented in a way that leans heavily on the material presented in Chapter 11. Finally,
radiation is discussed at length in Chapter 13. We emphasize how the concept of a
stationary state is not at odds with the classical concept of radiation from accelerating
charges. Otherwise, however, the presentation in this chapter is standard, but, we hope,
thorough.