Functional approach to scattering in quantum mechanics

Abstract

A functional approach to scattering theory in quantum mechanics is developed by deriving an explicit functional expression fortransition amplitudes. In applications, the formalism avoids dealing with noncommutativity problems of operators, solving the Schrödinger equation (or the integral equation of the Green's function), or dealing with the often quite complicated continual (path) integrals and, most importantly, applies to short- and long-range interactions. The basic idea is the use of the quantum action principle followed by a systematic analysis of the concept of an intervening source developed earlier in the study of stimulated emission. A comparison with the standard approach is also made.