Caustic problems in quantum mechanics with applications to scattering theory

We present a detailed discussion of the semiclassical approximations to path integrals when there exist caustics in the relevant family of classical trajectories. We show carefully how the Airy functions arise from the post-semiclassical approximation of the path integral and interpret the coefficients in the Airy functions in terms of the flow of classical trajectories. Finally, we present a configuration-space path integral for the scattering matrix and extend our discussion of caustics to the case of rainbow scattering.