ARTHUR HAAS. Materiewellen und Quantenmechanik. Leipzig. Akademische Verlagsgesellschaft 1928. VIII + 160 pp.

A. Haas. Matter Waves and Quantum Mechanics.

The need for an elementary exposition of the foundations of the new quantum mechanics is very great. Quantum theory touches on questions with which the experimental physicist, the physical chemist, and the astronomer are, in practice, directly occupied. Apart from the natural, justified interest in the theory, the desire to master it is dictated by the demands of current experimental work. It is hardly worthwhile at present to strive to popularize quantum mechanics for very broad circles. The theory is still in a stage of rapid growth; much in it is still unclear, often changes and is corrected; moreover, the theory is extremely formal and abstract. But for specialists, or for those intending to ...

as such, a simplified exposition of the elements of the new quantum mechanics is needed already now.

A successful attempt in this direction has been made in the book under review. In the realm of quantum phenomena, where it becomes necessary to speak of the “fundamental unobservability” of elementary processes, it is of course hopeless—at least at present—to apply the usual popularizing device of visual analogies and models. Here the only possible aim is to simplify and make more intuitive the mathematical apparatus. It is along this rational path that Haas proceeds: he popularizes the mathematics of Schrödinger’s and Heisenberg’s theories chiefly by explaining it through individual, very simple examples. Haas’s simplified proofs, derivations, and generalizations hardly satisfy mathematical rigor, but one may hope that such inaccuracies will not mislead the reader. A reader who knows the elements of analysis will obtain a convex, though not entirely exact, idea of what characteristic functions are in Schrödinger’s theory, what matrices are in Heisenberg’s theory, the new Fermi statistics, and so on.

The book is very small in size, but contains 16 chapters, each with very rich content. It is enough to point out that, in addition to presenting the theories of de Broglie, Schrödinger, and Heisenberg, it gives a fairly substantial account of Pauli’s “exclusion,” Bose and Fermi statistics, presents the author’s own considerations on the connection between wave mechanics and the theory of relativity, and briefly touches upon the latest results of the theory. It is clear that, with such a ratio of size to content, the book must be in the nature of a synopsis. But this synopsis is clear and is read from beginning to end with great interest. Of course, in such a book one can point to many important omissions, but in the end one is forced to be surprised that there are nevertheless not as many of them as might have been expected a priori.

A Russian translation of Haas’s book, especially with some additions, would be very useful.

S. Vavilov.