Global, uniform semiclassical approximations for quantum systems on the half line.

Motivated by recent experiments on highly-excited Rydberg atoms in electrically polarized states, we consider the semiclassical analysis of quantum systems defined on the interval 0 X infinity. Caustics plague the conventional approach, and Maslov's technique cannot be used. Instead we introduce an affine phase- space formulation that leads to a global, uniform semiclassical approximation to the wave function which fully captures the effects of caustics.