A process of operator replacement leads to a generalization of Schrodinger’s equation to curved space-time, linking general relativity and quantum mechanics in a natural way. This fourth-order equation, which reduces and specializes to the Klein-Gordon equation in the flat space limit, must be solved in tandem with the Einstein field equations with suitable stress-energy. The flat space propagator, for large momenta, varies as1/p4,meaning that divergences should be less problematic than in standard theories. Approximate solutions can be obtained for static, spherically-symmetric scalar fields. ©1999 American Institute of Physics.