Bibliography

D. I. Blokhintsev, Introduction to Quantum Mechanics, Gostekhizdat, 1944. Price 18 rubles. 430 pp.

Among the Russian-language literature on quantum mechanics, Prof. D. I. Blokhintsev’s Introduction to Quantum Mechanics is, in essence, the first university textbook to present the material sufficiently fully, systematically, and at a quite modern scientific level.

The practice of teaching quantum mechanics in universities has led to a more or less definite range of questions that can and should be covered in a university course. These are precisely the questions considered in Blokhintsev’s book. Here is a brief list of them: the fundamental ideas of quantum mechanics, the mathematical apparatus of quantum mechanics, the harmonic oscillator, the hydrogen and hydrogen-like atoms, diatomic molecules, the motion of an electron in a periodic field, electron spin, perturbation theory with applications to the Stark and Zeeman effects, the theory of particle collisions, quantum transitions, optical effects, the passage of particles through potential barriers, the theory of systems of particles, secondary quantization and quantum statistics, many-electron atoms, chemical and molecular forces, and magnetic phenomena. Questions of relativistic quantum mechanics are not touched upon at all in the book under review, and, on the contrary, it seems to us that one need not object to this, since presenting these questions in the style required for a textbook would, in view of the excessive length and even more so the scope of the book, be unreasonable (430 pages).

The general arrangement of the material should be acknowledged as successful. First the general basic ideas of quantum mechanics are set forth, and in connection with this the mathematical apparatus is developed; then, on this basis, a variety of applications are considered. Undoubtedly, studying this book will make it possible to proceed to independent research work in the field of applications of nonrelativistic quantum mechanics.

However, the book contains a number of serious shortcomings. First of all, one must note a certain carelessness of presentation, which is manifested in a large number of errors, unclear formulations, and poorly edited passages. All this creates serious difficulties when reading the book, especially for students. Let us give several examples.

In § 25 an incorrect definition of angular momentum is given, and further on some of the formulas are written correctly, while others are written incorrectly, which produces considerable confusion.

On p. 99 it is stated that Ehrenfest’s theorems show that, for the mean values of momenta and coordinates, the classical equations of mechanics are valid. This is incorrect and contradicts what is said later, on pp. 101–103, where Newton’s equations of motion are derived from the quantum equations.

On pp. 257–258 calculations are given of the atomic factor for the scattering of fast electrons, and, as is usually done, this is carried out indirectly by bypassing the difficulties associated with the presence of a divergent integral. However, no attention is drawn to this and the legitimacy of the procedure is not shown; if a thoughtful reader attempts to carry out the calculations by a direct method, he will obtain an entirely different result, which will lead him into a dead end. This kind of exposition is unsuitable for textbooks.

Sometimes an unclear exposition of an issue leads to incorrect conclusions. Thus, for example, on p. 66 there is a brief discussion of the analytic requirements imposed on wave functions, in particular their finiteness and single-valuedness. From the author’s exposition one gets the impression that these requirements follow from the statistical interpretation of wave functions. In fact, however, this follows from the requirement of self-adjointness and, in a certain sense, closedness of the operators considered in the theory. Perhaps the textbook should not analyze these difficult questions in detail, but it is necessary to state clearly what the essence of the matter is.

Of course, all these shortcomings are easily remedied. There is no doubt that now, when ways have been found for the practical use of intranuclear energy, the teaching of quantum mechanics will expand still further and deepen. It is possible that a new edition of Prof. Blokhintsev’s textbook will be needed, and, of course, after its defects have been eliminated it will satisfy new and higher requirements as well. It seems to us only that, in doing so, it would be desirable to include some elementary questions of the theory of the atomic nucleus (for example, the theory of the deuteron, the Wigner theory of light nuclei, etc.).

The author’s treatment of the fundamental questions of quantum mechanics should be considered separately. This is a far subtler and more complex matter. They are almost entirely concentrated at the beginning of the book, in Chapter III. It seems to us that it is written too tersely and is difficult for beginners. Perhaps some questions should have been examined in greater detail in later chapters, and here specific examples or certain paradoxes should have been analyzed in more detail. Thus, for example, it would have been very useful to analyze clearly and in detail the discussion between Einstein and Bohr, the study of which makes it possible to understand more precisely and subtly the statistical character of quantum mechanics, the distinction between mixed and pure ensembles, and a number of other important questions. Further, it should be noted that, when discussing the question of the mutually exclusive character of the measurement of momentum and coordinate, it is not shown that physical instruments are in fact so constructed that an instrument suitable for measuring the coordinate is not suitable for measuring the momentum, and conversely.

The point, however, lies not so much in individual shortcomings as in the general style of presentation of the questions. Of course, these questions are among the most difficult in quantum mechanics, difficult both to understand and to present. It may be that in this area not everything has yet been fully clarified and worked out. In such a situation, it would have been advisable, as far as possible, to show more prominently the difficulties encountered here, to show clearly the struggle of different points of view surrounding these questions, and to illustrate visually their whole acuteness. The author, however, has taken a different path. He in fact glosses over all the difficulties present here and tries to present everything in such a form as though there were no sharp points or controversial problems here at all. And since in reality the matter is otherwise, and from the author’s exposition the reader nevertheless cannot fully understand all these questions, the uninitiated reader, almost from the very beginning of his work on the book, is left with a harmful feeling of self-doubt, which hinders further work. It is precisely in this that we see the fundamental shortcoming of the reviewed textbook, which is in general not a bad one; and it is precisely here that the author’s particular attention should be directed in the further revision of the book.

A. G. Samoilovich