LOUIS DE BROGLIE, Théorie de la quantification dans la nouvelle mécanique, Paris 1932.
LOUIS DE BROGLIE, The Theory of Quantization in the New Mechanics, Paris 1932.

In de Broglie’s new book are collected and developed the lectures that the author delivered at the Henri Poincaré Institute in the fall semester of 1929–1930. It should not be confused with the previously published “Introduction to Wave Mechanics,” which appeared first in German and then in French. These two books of de Broglie’s, though they sometimes overlap, are in no way connected with one another.

The first part of the book serves, as it were, as an introduction to the principal second part. This part is devoted to the origin of the idea of quantization (Planck, Bohr); to the basic principles of classical mechanics, to which, incidentally, rather less space is allotted here than in de Broglie’s first book; to the traditional comparison of the equations of mechanics and optics; and to Schrödinger’s theory (for the case of one and several particles), with some examples of quantization (rotator, oscillator, hydrogen atom). Despite the general coherence and persuasiveness of the exposition, the basic idea—the idea of corpuscular-wave parallelism, belonging to de Broglie himself—is introduced dogmatically, and to a reader not yet accustomed to this idea it seems unnatural. Evidently this is because de Broglie, confining himself to a formal analogy between the equations of mechanics and optics, scarcely touches at all upon the dualism already indicated in the question of the nature of light. Thus the fundamental idea of wave mechanics is introduced not at all in the way de Broglie did it in his original work nine years earlier.

The second part is devoted, above all, to the mathematical apparatus of the new mechanics: vectors in \(n\)-dimensional space; complex vectors; functional space; operators and matrices. The second and third parts comprise: continuous matrices; Dirac’s function; the role of mean values in wave mechanics; the uncertainty relation; the case of mecha-

mechanical systems subjected to the action of external fields constant in time, and operators that do not depend on time, and the case of nonconservative systems with operators that are functions of time. The book does not touch on questions connected with the spin of the electron (as, incidentally, does Marx’s well-known book); the practically very fruitful theory of barriers is likewise absent (again, as in Marx).

Possessing approximately the same incompleteness as Marx, and serving, like Marx, as a student textbook, de Broglie’s book—not to mention the fact that it is more up to date—is far deeper than Marx’s book. At the same time it reads very easily; quite imperceptibly, almost without any strain, the reader not only penetrates the basic ideas but also begins to feel the nuances. The mathematics—the book is highly mathematical—is offered as though incidentally, even in chapters specially devoted to mathematical questions. With great skill the reader finds himself surrounded by the whole arsenal of matrices and operators, easily passing through the barrier of the usual “mathematical introductions” that separate the experimental physicist from wave mechanics. Throughout all seventeen chapters, rather serious questions acquire a simple and palpable form and are laid down in the reader’s memory with definite precision and clarity. Depth of ideas is combined with an elegance of exposition so characteristic of French authors.

F. Wülfenstein