Relativity and quantum mechanics

Conditions under which quantum mechanics can be made compatible with the curved space-time of gravitation theories is investigated. A postulate is imposed in the formv=v _g wherev is the kinematical Hamilton-Jacobi (geometric optic limit) velocity andv _g is the group velocity of the waves. This imposes a severe condition on the possible coordinates in which the Schrödinger form (the coordinate realization) of quantum mechanics can be set up for purposes of calculating observable effects. Some such effects are calculated for a class of theories and are compared with experiments.