Theory of Reactive Collisions: Conformal Transformation

Abstract

Conformal mapping techniques are applied to the Schrödinger equation for a bimolecular exchange reaction, with all three atoms lying on a line. For the case of a very heavy central mass, the extension of the theory to three dimensions is indicated. An angle‐shaped region of the potential‐energy surface is mapped onto an infinite strip in order to simplify the theoretical treatment of the boundary conditions. The mapping function is determined with the help of the Schwarz–Christoffel formula, and its properties described. The transformed Schrödinger equation is converted into an integral equation using the method of Green's functions, and integral representations for the reflection and transmission coefficients are obtained.