Résurgence d'un thème de Huygens-Fresnel. (The resurrection of a topic of Huygens-Fresnel)
By invoking a correspondence between the classical equations governing the propagation of light and the Hamilton-Jacobi equation, an interpretation of wave mechanics in terms of the theory of geometric optics is suggested. This leads to applications of the Huygens-Fresnel principle, catastrophe theory and semi-classical theory to quantum mechanics. Some of this work is new and it also embodies results which are already well-known. Interesting examples of the approach are given which give rise to the Huygens-Fresnel integrals and by local confluence to the Airy and Weber functions. This work will certainly stimulate further research into the theory of semi-classical approximation in wave mechanics.
scientific article; zbMATH DE number 4127765