Topics in atomic physics

НазваниеTopics in atomic physics
Дата конвертации02.02.2013
Размер7.95 Kb.

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


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.

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