Bibliography

M. Born. Vorlesungen über Atommechanik. Erster Band. Pp. IX + 358; J. Springer, Berlin, 1925.

M. Born. Lectures on Atomic Mechanics.

The second volume of the extraordinarily interesting planned series “Struktur der Materie,” edited by Born and Franck, was written by Born and bears the title Vorlesungen über Atommechanik. The book is a reworking of lectures delivered by the author in Göttingen. However, the numerous examples and calculations undertaken by Born’s assistant Hund have considerably expanded the scope of the book, turning it into a systematic textbook on the foundations of the mechanics of the atom. As the title itself indicates, the purpose of the book is to give a deductive theory of the atom, considering the motions of electrons in the field of the nucleus from the standpoint of mechanical (and electrodynamical) principles, much as celestial mechanics is concerned with elucidating the motion of heavenly bodies governed by Newton’s laws. The author therefore begins with an exposition of the basic methods of mechanics, especially those suitable for developing problems in whose solution quantum restrictions play an essential role (the Hamilton–Jacobi theory). Throughout almost the entire book this method of formulating and solving the mechanical problem is maintained, with subsequent restrictions dictated by quantum theory. The latter is introduced in its pure, so to speak “classical,” form, without those compromises whose necessity has recently been shown by the work of Bohr, Lande, Heisenberg, and Born. The adiabatic hypothesis of Ehrenfest and the correspondence principle are set forth very clearly. Finally, considerable attention is devoted to the development of the foundations of perturbation theory and to its application to the theory of the atom in the form developed in the works of Born himself. Thus questions that were treated episodically and very incompletely in the mathematical appendices to Sommerfeld’s Atombau und Spektrallinien receive here a systematic treatment. Conversely, the entire extensive experimental material that constitutes the value of Sommerfeld’s book is assumed to be known and is presented in a brief introduction only as a reminder. Therefore the books of Born and Sommerfeld, taken as a whole, constitute a concise but fairly complete encyclopedia.

Bibliography

of the modern doctrine of the atom. Of course, the continuous advance in this field of knowledge makes ever new additions necessary. Entire monographs are devoted to certain special questions (for example, Back and Landé); other facts are incorporated into new editions of Sommerfeld’s ever-expanding book. On the theoretical side the situation is somewhat different. The material set forth in the book under review may be regarded as almost fully established. But it is likewise beyond doubt that the mathematical theory of the atom in this form is not only unfinished, but even not correct. And the new paths along which the development of the theory will proceed—the very changes in the principles of the quantum theory of the atom—are at present only barely being indicated (Bohr, Kramers, Heisenberg, Born). In the author’s conception, the mechanics of the atom as written should constitute only a first volume. The second volume might become the “higher approximation” to the definitive mechanics of the atom. It will probably be quite a few years before this second volume is written. For anyone seriously engaged in the study of atomic theory, Born’s book will be very useful. The exposition is concise, but complete and clear; it may be somewhat difficult for beginners, but it is exceedingly satisfactory by virtue of its systematic character. The appearance—as always with Springer—is impeccable; the price—also as always—is high.

Gr. Landsberg.