Path integrals and semiclassical approximations to wave equations.

In the parabolic approximation the wave equation resembles a Schrodinger equation and thus its solution admits a path integral representation. For certain applications, including those involving random media that allow a Markov approximation, a stationary-phase approximation often affords an adequate evaluation of the path integral. We discuss the stationary- phase approximation for both the configuration-space and coherent- state representation path integrals, and show that, unlike the former, the latter formulation offers a uniform approximation and leads to no unphysical divergences at caustics as a matter of principle. The result is a novel form of semiclassical approximation to wave equation solutions.