  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
non-singular 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.
