  We present a general relativistic framework for studying gravitational
effects in quantum mechanical phenomena. We concentrate our attention on the
case of ultra-relativistic, spin-1/2 particles propagating in Kerr spacetime.
The two-component Weyl equation with general relativistic corrections is
obtained in the case of a slowly rotating, weak gravitational field. Our
approach is also applied to neutrino oscillations in the presence of a
gravitational field. The relative phase of two different mass eigenstates is
calculated in radial propagation, and the result is compared with those of
previous works.
