Pham, Frédéric Résurgence d’un thème de Huygens-Fresnel. (The resurrection of a topic of Huygens-Fresnel). (French) Zbl 0688.35093 Publ. Math., Inst. Hautes Étud. Sci. 68, 77-90 (1988). 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. Reviewer: H.Exton Cited in 6 Documents MSC: 35Q99 Partial differential equations of mathematical physics and other areas of application 35F20 Nonlinear first-order PDEs 58J90 Applications of PDEs on manifolds Keywords:Hamilton-Jacobi equation; semi-classical theory; quantum mechanics PDFBibTeX XMLCite \textit{F. Pham}, Publ. Math., Inst. Hautes Étud. Sci. 68, 77--90 (1988; Zbl 0688.35093) Full Text: DOI Numdam EuDML References: [1] G. I. Airy, On the Intensity of Light in the neighbourhood of a caustic,Trans. Camb. Phil. Soc.,6 (1838), 379–402. [2] V. I. Arnold, Integrals of rapidly oscillating functions and singularities of the projections of Lagrangean manifolds,Funct. Anal. and its Appl.,6, 3 (1972), 61–62. [3] V. I. Arnold, Remarks on the method of stationary phase and Coxeter numbers,Usp. Mat. Nauk,28, 5 (1973), 17–44. [4] R. Balian, C. Bloch, Solution of the Schrödinger equation in terms of classical paths,Ann. of Physics,85 (1974), 514–545. · Zbl 0281.35029 [5] M. V. 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