Semiclassical time-dependent propagation in three dimensions for a Coulomb potential

A unified semiclassical time propagator is used to calculate the semiclassical time-correlation function in three Cartesian dimensions for a particle moving in an attractive Coulomb potential. It is demonstrated that under these conditions the singularity of the potential does not cause any difficulties and the Coulomb interaction can be treated as any other nonsingular potential. Moreover, by virtue of our three-dimensional calculation, we can explain the discrepancies between previous semiclassical and quantum results obtained for the one-dimensional radial Coulomb problem.