  We give a systematic treatment of the quantum mechanics of a spin zero
particle in a combined electromagnetic field and a weak gravitational field,
which is produced by a slow moving matter source. The analysis is based on the
Klein-Gordon equation expressed in generally covariant form and coupled
minimally to the electromagnetic field. The Klein-Gordon equation is recast
into Schroedinger equation form (SEF), which we then analyze in the
non-relativistic limit. We include a discussion of some rather general
observable physical effects implied by the SEF, concentrating on
gravitomagnetism. Of particular interest is the interaction of the orbital
angular momentum of the particle with the gravitomagnetic field.
