Semiclassical Theory—Path Integrals

L. E. Reichl

Edward Shuryak

Gerhard Dangelmayr, W. Güttinger, W. Veit

Bruce L. Nelson

We present a well-defined path integral for scattering theory. This path integral is particularly well suited for evaluating the semiclassical expansion for the cross section. As an example, we show how the semiclassical cross section for rainbow scattering can be obtained in a systematic fashion. We indicate how the path-integral approach to semiclassical scattering theory may be more general and more reliable than other approaches.

L. E. Reichl

Alvin P. Penner, R. Wallace

The evaluation of a Feynman path integral is discussed for a scattering problem in which some degrees of freedom of the system are treated classically, while others are treated quantum mechanically. The path integral is of the type $K(0, {t}^{\ensuremath{'}\ensuremath{'}}; 0, {t}^{\ensuremath{'}})$, and is of interest in a multichannel semiclassical collision theory previously developed by Pechukas. It is shown that this path integral can be evaluated precisely in practice, despite the presence of noncausal terms in the integrand.