Numerical calculation of the relativistic acceleration of an electron in   curved spacetime using the Dirac equation
  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. 
J.D. Franson
gr-qc quant-ph