Multiple surface molecular motion: A t-matrix approach

Abstract

Sets of coupled differential equations encountered in quantum mechanical scattering theory are converted to integral equations by means of a Wentzel-Kramers-Brillouin type Green's function. The residual terms are analyzed and it is shown that the resulting set of integral equations may be well approximated by a low order Fredholm expansion. The saddle point method for the approximate evaluation of integrals is seen to be equivalent to a replacement of the residual terms with a separable potential of low rank. Applications to scattering problems and chemical reactions are pointed out.