Résurgence d'un thème de Huygens-Fresnel. (The resurrection of a topic of Huygens-Fresnel)
type: Item
instance of: scholarly article
title: Résurgence d'un thème de Huygens-Fresnel. (The resurrection of a topic of Huygens-Fresnel)
zbMATH Open document ID: 0688.35093
DOI: 10.1007/BF02698542
author: Frédéric Pham
published in: Publications Mathématiques
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/104044
review text: 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.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 58J90
zbMATH DE Number: 4127765
zbMATH Keywords: Hamilton-Jacobi equation
zbMATH Keywords: semi-classical theory
zbMATH Keywords: quantum mechanics
reviewed by: H. Exton
MaRDI profile type: Publication
cites work: Solution of the Schrödinger equation in terms of classical paths
cites work: Q3251584
cites work: Q4765553
cites work: Oscillatory integrals, lagrange immersions and unfolding of singularities
cites work: Fourier integral operators. I
cites work: On holonomic systems of microdifferential equations. III: Systems with regular singularities
cites work: A study of Feynman integrals by micro-differential equations
cites work: A WKB-Type Approximation to the Schrödinger Equation
cites work: Caustiques, phase stationnaire et microfonctions
cites work: Transformées de Laplace des microsolutions de systèmes holonomes. (Laplace transforms of microsolutions of holonomic systems)
cites work: Q4403324
cites work: Q3041568
cites work: Q3844537
description: scientific article; zbMATH DE number 4127765