  The relativistic acceleration of an electron in a uniform gravitational field
is calculated numerically using the generalization of the Dirac equation to
curved spacetime. Equivalent results are also obtained analytically using an
iterative approach that is not based on the WKB approximation, which has been
used extensively in the past. The acceleration is found to be proportional to a
factor of $(1-3v^2/c^2)$ using Schwarzschild coordinates, which is consistent
with the classical geodesic of a particle. These techniques may be useful in
resolving the differences between commonly-used approximations.
