Abstract
To determine the photon emission or absorption probability for a diatomic system in the context of the semiclassical approximation it is necessary to calculate the characteristic canonical oscillatory integral which has one or more saddle points. Integrals like that appear in a whole range of physical problems, e.g., the atom–atom and atom–surface scattering and various optical phenomena. A uniform approximation of the integral, based on the stationary phase method is proposed, where the integral with several saddle points is replaced by a sum of integrals each having only one or at most two real saddle points and is easily soluble. In this way we formally reduce the codimension in canonical integrals of “elementary catastrophes” with codimensions greater than 1. The validity of the proposed method was tested on examples of integrals with three saddle points (“cusp” catastrophe) and four saddle points (“swallow-tail” catastrophe).
Subject
Condensed Matter Physics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics
Reference20 articles.
1. The mathematical physics of rainbows and glories
2. Topological models in biology
3. Stabilité Structurelle et Morphogénèse. Essai d’une Théorie Générale des Modèles;Thom,1971
4. Catastrophes and molecular collisions
5. Integrals with coalescing saddles;Berry,2010
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献