A. SOMMERFELD. Atombau und Spektrallinien. Wellenmechanischer Ergänzungsband. Fr. Vieweg. Braunschweig, 1929. Pp. X + 351. RM. 14.50.

A. SOMMERFELD. The Structure of the Atom and Spectra. Supplementary Volume—Wave Mechanics.

The purpose and character of this book are formulated so clearly by the author himself that it will be most expedient to give here the following extensive excerpt from the preface:

“I have called this supplementary volume ‘wave-like,’ since Schrödinger’s methods, in practical use, possess advantages over the specific methods of ‘quantum mechanics.’ For me, however, there is no doubt that the general ideas which led Heisenberg to the establishment of quantum mechanics are also necessary for wave mechanics.

Schrödinger’s original point of view, according to which transitions must occur only between coexisting states, is obviously too narrow; therefore I have transferred to wave mechanics the consideration of states and transitions, just as admissible as was provided by Heisenberg from the very beginning. But this means renouncing the broad goals which Schrödinger and de Broglie set themselves, and renouncing visualizability in favor of formalism. The electron remains, in wave mechanics as well, ultimately a point charge, and the light quantum a point center of energy. But the dualism between the light quantum and the light wave extends also to the corpuscle: alongside the corpuscular electron we encounter the electron-wave, whose existence is confirmed by experiments that are multiplying every day.

For several semesters I have tried in my university lectures to present, for myself and for my listeners, the principal results of wave mechanics in as simple a form as possible. It turned out that in all cases which admit complete integration, the polynomial method is sufficient; without special assistance from the theory of functions it leads to final analytical expressions. On the other hand, the method of ‘generating functions,’ which is often very elegant but always gives the intensity integrals by a somewhat artificial route, can be replaced by the direct application of the orthogonality conditions. In view of this I have made the basis of the present exposition these viewpoints, though not very profound, yet uniform and simplifying. Far more substantial is the simplification which is achieved in the theory of the electron developed by Dirac. The method applied here by me almost completely eliminates four-dimensional matrices and reduces the matter to two-dimensional matrices, which admit a geometrical interpretation.

As reader I had in mind, as in the previous editions, physicist-experimenters and theoreticians in equal measure. Therefore I have chiefly confined myself to those problems which present ne-

Bibliography

…of immediate physical interest. The general speculations of the transformation theory concerning probabilities are considered very briefly, as are the fundamental questions of inaccuracy and observability. These general questions, as I have heard, will soon be the subject of books by other competent persons. I wished above all to adhere to the character of my book and, consequently, to dwell as far as possible on concrete questions.”

It remains for us to add to this only purely external information about Sommerfeld’s new book. The book is divided into two extensive chapters, of which the first (pp. 1–169) is devoted to the foundations of wave mechanics and to some of its simplest applications (oscillator and rotator, the problem of the hydrogen atom, the simplest problems of the theory of molecules). The second chapter (pp. 169–340) is devoted to more difficult problems and bears the title “The Problem of Perturbation and Diffraction. The Rotating Electron.” It contains an exposition of the following questions: 1) Schrödinger’s perturbation theory; 2) the theory of the Stark effect; 3) dispersion theory; 4) the photoelectric effect; 5) the problem of the collision of two particles; 6) diffraction of electron waves; 7) the Compton effect; 8) the problem of heat; 9) interpretation of classical quantities from the point of view of wave mechanics; 10) the nature of the electron.

The book is written with Sommerfeld’s characteristic mastery: convexly, concisely, and clearly. Together with the main volume, this supplementary volume to Atomic Structure will, of course, serve as a reference book for all physicists interested in the problems of contemporary atomic theory.

Э. Ш.