On the equivalence of the classical-limit scattering matrix to the Wentzel-Kramers-Brillouin formalism

Abstract

The classical-limit scattering matrix (CLSM) formalism was developed by Miller as a simple semiclassical procedure for the analyses of complex scattering and reaction processes. It invokes simple classical dynamics to define trajectories and superposition procedures to obtain interference effects. In one-dimensional systems, Miller (1974) has shown that the CLSM is equivalent to the standard WKB approximation. In this paper, it is shown that the equivalence between the CLSM and WKB extends to general systems. This equivalence between the WKB and CLSM formalisms is attributed to the general equivalence of the h(cross)-expansion procedure in the WKB with the stationary phase approximation used in the CLSM.