BRILLOUIN, LÉON.- THE INDTRODUCTION OF THE "WKB METHOD" IN QUANTUM MECHANICS.

La mécanique ondulatoire de Schrödinger; une méthode générale de résolution par approximations successives.

Paris, Gauthier-Villars et Cie, 1926. 4to. Without wrappers. In: "Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences", Tome 183, No 1. Pp. (5-) 100. (Entire issue offered). Brillouin's paper: pp. 24-26.

First appearance of Brillouin's importent paper in which he introduced the WKB-method in quantum Mechanics.

"In 1925 Brillouin was the only French theoretician to react competently to Werner Heisenberg’s new matrix mechanics. In two papers published in 1926, he contributed to the exploration of the mathematical content of Heisenberg’s theory. Brillouin’s first contribution in this field was important (the paper offered). Through a new method of semiclassical approximation, he discovered the relation between Schrodinger’s mechanics and the quantum theory of Niels Bohr and Sommerfeld. Presumably inspired by de Broglie’s early analogies between mechanics and optics, he found this approximation as the quantum mechanical counte)t of the approximation. In this procedure, stationary solutions of the Schrödinger equation are sought in the form eiS/h (as in the eikonal approximation of optics). In the first approximation (h small), S must be a solution of the Hamilton-Jacobi equation of classical mechanics, and the Bohr-Sommerfeld conditions (S = 2pnh on a closed trajectory) must be satisfied for the W function to be defined and singlevalued in all space. Subsequent corrections are proportional to successive powers of h. They intermix the various Bohr trajectories. thereby reintroducing the complex interplay of quantum states found in matrix mechanics, This method, published by Brillouin in July 1926 - anticipated by Harold Jeffreys in 1923 in a purely mathematical context, reinvented by Gregor Wentzel in September 1926. and perfected by Hendrik Kramers in November 1926 - is now called the (J) BWK method and is widely used in many quantum mechanical problems."(DSB).
See also Max Jammer "The Conceptual development of Quantum Mechanics", pp. 277 ff.

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