  The Klein-Gordon equation for the wave function of a single massive scalar is
written in spherical and parabolic coordinates in the presence of a
Schwarzschild background, and some semi-classical techniques for deriving
asymptotic results are considered. In addition to the well-known logarithmic
phase shift due to the tortoise radial coordinate, it is found that there is a
mass-dependent logarithmic phase shift at infinity. This is found to be
necessary to match the Newtonian cross-section in the non-relativistic limit.
Finally, by imposing suitable boundary conditions near the horizon, the phase
shift is calculated.
