Covariant Feynman derivation of Schrodinger's equation in a riemannian space

Ruse's covariant Taylor expansion is used to give a neat and rapid derivation of the covariant Schrodinger equation for a particle moving in a riemannian space. It is pointed out that the calculation is basically the same as Kolmogorov's derivation of the diffusion equation, and a covariant form of the stochastic differential equation is given.