Semiclassical approximations to the coherent-state propagator for a particle in a box

We compute the semiclassical coherent-state propagator for a particle moving in a one-dimensional box. In this semiclassical approach complex trajectories are stationary paths of the propagator{close_quote}s asymptotic expansion and play a fundamental role. A second semiclassical approximation is also introduced, which makes use of real trajectories only. An application to a seemingly simple system, the infinite well, is carried out completely for the diagonal elements, and a comparison is made among the three possible methods, those based on complex and real trajectories and the {open_quote}{open_quote}exact case{close_quote}{close_quote} that is determined by decomposing the propagator into its eigenstates. {copyright} {ital 1996 The American Physical Society.}