Wigner E.P. Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra

Revised Edition. — New York, London: Academic Press, 1959. — XI, 372 p. — (Pure and Applied Physics Series, Volume 5).The purpose of this book is to describe the application of group theoretical methods to problems of quantum mechanics with specific reference to atomic spectra. The actual solution of quantum mechanical equations is, in general, so difficult that one obtains by direct calculations only crude approximations to the real solutions. It is gratifying, therefore, that a large part of the relevant results can be deduced by considering the fundamental symmetry operations.Group Theory: And Its Application To The Quantum Mechanics Of Atomic Spectra aims to describe the application of group theoretical methods to problems of quantum mechanics with specific reference to atomic spectra. Chapters 1 to 3 discuss the elements of linear vector theory, while Chapters 4 to 6 deal more specifically with the rudiments of quantum mechanics itself. Chapters 7 to 16 discuss the abstract group theory, invariant subgroups, and the general theory of representations. These chapters are mathematical, although much of the material covered should be familiar from an elementary course in quantum theory. Chapters 17 to 23 are specifically concerned with atomic spectra, as is Chapter 25. The remaining chapters discuss topics such as the recoupling (Racah) coefficients, the time inversion operation, and the classical interpretations of the coefficients. The text is recommended for physicists and mathematicians who are interested in the application of group theory to quantum mechanics. Those who are only interested in mathematics can choose to focus on the parts more devoted to that particular area of the subject.This translation of the well-known book published by Wigner in 1931 is to be warmly welcomed. Of the first half of the book about 60 pages are devoted to matrix theory and to a resume of the relevant parts of quantum mechanics and about 120 pages to the theory of groups and their representations. The remainder of the book is concerned with the application of group theory to atomic spectra and includes three additional chapters dealing with developments, such as time inversion and the Racah coefficients, which have been made since the original publication of the book. The whole book is written with the utmost clarity, and a student wishing to acquire, for any purpose whatever, a knowledge of elementary group theory including the theory of the symmetric and the rotation groups, could not do better than read the 120 pages referred to above.Wigner's book (published in 1959) is an expanded and revised English translation of the book originally published in German in 1931. Starting from vectors and matrices the author moves on to the description of abstract group theory and its application to atomic spectra. This is a classical reference in the field of quantum mechanics and atomic physics which should be consulted by most physicists and chemistsThis is the classic, timeless text on group and representation theory as applied to atomic spectra with treatments of angular momentum in quantum mechanics, selection and intensity rules with electron spin, fine structure of spectral lines, and Racah coefficients. Wigner's is still an ideal introductory text.