Bibliography

New Textbooks on Quantum Mechanics

1. CLEMENS SCHAEFER. Einführung in die theoretische Physik. Dritter Band. Zweiter Teil: Quantentheorie. Pp. VIII + 510. Walter de Gruyter & Co. Berlin und Leipzig, 1937.

2. EDWIN C. KEMBLE. The Fundamental Principles of Quantum Mechanics. Pp. XVIII + 611. McGraw Hill. New York, 1937.

3. SAUL DUSHMAN. The Elements of Quantum Mechanics. Pp. XII + 452. J. Wiley & Sons. New York, 1938.

The extensive literature of monographs and textbooks on quantum mechanics was supplemented, at the end of 1937 and in 1938, by a number of new books, predominantly of textbook character (in addition to those listed above, at the end of 1938 V. Rojansky’s book appeared in America).

1. Cl. Schaefer’s book is the final part of the last volume of his course in theoretical physics. Over the course of 25 years (the first volume appeared in 1914) the author has carried out the enormous labor of compiling a comprehensive manual covering all of theoretical physics, beginning with classical mechanics and ending with atomic theory and quantum mechanics. The merits of this manual, its completeness, and its great pedagogical value are well known. The Russian translations of parts of Schaefer’s book (mechanics, thermodynamics and statistics, electrodynamics and optics) have been of great benefit to our physics students, graduate students, and teachers.

A peculiarity of the presentation of quantum mechanics in Schaefer’s book is that half of it is devoted to a detailed exposition of Bohr’s theory. The question of the place that Bohr’s theory should occupy in a contemporary course of quantum mechanics is a very controversial one. Familiarity with this theory is, in our opinion, necessary for a clear understanding of the further development of quantum mechanics. However, it is hardly expedient to make the reader pass through all the stages of the historical development of a theory, stopping at these stages with the same thoroughness that was necessary before a more perfect theory appeared. It would have been possible to show the reader the fruitfulness of Bohr’s theory and, at the same time, to reveal its weak sides and convince him of the inevitability of a further step in the same direction on a smaller number of pages.

The second half of the book is devoted specifically to the new quantum mechanics and contains the following material: the foundations of wave mechanics (de Broglie’s theory and Schrödinger’s equation), the simplest applications of wave mechanics (including perturbation theory and the helium problem), its statistical interpretation, radiation, and Dirac’s theory.

Schaefer’s exposition reveals the author’s awareness: it is extremely conscientious, but lacks originality even in the pedagogical respect. Contrary to the manner of presentation in the preceding volumes, in this volume—which by the very nature of the subject presents the greatest difficulties for the reader—Schaefer often confines himself to brief remarks where more detailed explanations would be needed (see, for example, the exposition of the polynomial method in

VI). The general impression is that the last volume of Schaeffer’s book is considerably weaker than the preceding ones.

1. Kemble’s book is intended for the prepared reader. The author set himself the task of giving a critical exposition of the foundations of quantum mechanics; the professor and player do not play a subordinate role in Kemble’s book. The author is interested above all in the strict logical foundation of the theory, and in a critical examination of its premises and mathematical methods. In order to make the reader’s work easier, the book includes an exposition of many purely mathematical questions: here one may find not only very serious topics, acquaintance with which may be lacking even in the prepared reader (function space, matrices, operators), but also quite ordinary questions of analysis, such as the Fourier integral. Much attention is also given to the concept of measurement, the uncertainty principle, and so on. There is no doubt that everything included in this book is set forth very carefully, all the necessary reservations are made, and the weak points in the logical and mathematical development of the theory are indicated. The author himself characterizes his aspirations as an attempt to find a path between the Scylla of superficiality and the Charybdis of tedious complexity. Unfortunately, one cannot agree with one of the American reviewers of this book (E. Condon), who remarked that the author’s path proved to be somewhat closer to Charybdis than to Scylla. For all its undoubted merits, the book does not reward the reader: having spent the effort to read six hundred pages of small print, he will not even reach Dirac’s equation, and only on the very last pages of the book will he obtain rather limited information about solving the helium problem in quantum mechanics and about exchange forces. He will derive no representation of the enormous variety of physical phenomena subject to quantum mechanics, or of its living and effective content. Kemble’s book—extensive and serious, written with great knowledge of the subject and love of rigor in formulation—has met a sad fate: it will rest on library shelves, and persistent readers who read it from beginning to end, one may say in advance, will not be many.

2. Dushman’s book is not only unlike Kemble’s, but in many respects is the opposite of it. Whereas the latter intended his exposition for the well-prepared reader, Dushman has in view assistance in a primary acquaintance with quantum mechanics. Unlike the well-known books of Haas and Darrow, Dushman does not confine himself to skimming the surface, but also tries to show, step by step, all stages of the calculations. He diversifies the examples of applications of quantum mechanics: alongside a firmly fixed quantum-mechanical “menu” (oscillator, rotator, central problem), he offers the reader more delicate dishes, such as van der Waals forces, the hydrogen molecule, chemical valence, and radiation problems.

A somewhat unpleasant impression is produced by the excessive compilatory character of the book. In some places it is even more reminiscent of a reader than of a coherent exposition. The author quotes, in quotation marks, excerpts taken from various textbooks, and moreover far from always classical ones (such as Leigh Page’s textbook of theoretical physics). His conscientiousness sometimes even arouses astonishment: having written the mathematical formulation of d’Alembert’s principle, he adds in quotation marks: “Lagrange laid this equation at the basis of all dynamics”; from a footnote the reader learns that these words are taken from Webster’s Mechanics. Such an elementary thought could perhaps have been expressed “in one’s own words”; and, moreover, Webster’s heirs would probably have made no claims against the author had he given this saying without quotation marks. We would not allow ourselves to mention this trifle if it were the only one; in the book one can find many analogous examples.

Dushman’s book, as indicated, is intended for the poorly prepared reader. There is no doubt, however, that the size of the book, the choice of mate-

material and the manner of its presentation always also determine the lower limit of the reader’s level of knowledge. We believe that someone who is little acquainted with elementary algebra will hardly begin to study a 500-page book on quantum mechanics filled throughout with formulas. Dushman is evidently aware of this deficiency, since he considers it necessary to recall (it is true, in an appendix) how quadratic equations are solved.

On the whole, despite the shortcomings indicated and the lack of rigor in the presentation, Dushman’s book will be useful to readers wishing to take their first steps in quantum mechanics. Its simple exposition, sufficient amount of material, and numerous references to the literature—all this will help anyone who wishes to become acquainted with this most important branch of modern physics, knowledge of which is becoming more and more necessary also for chemists, engineers, and all those seriously interested in the remarkable advances in the understanding of the nature of matter achieved over the last fifteen years.

E. Shpolskii, Moscow