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We investigate the quantum mechanical wave equations for free particles ofspin 0,1/2,1 in the background of an arbitrary static gravitational field inorder to explicitly determine if the phase of the wavefunction is $S/\hbar =\int p_{\mu} dx^{\mu} / \hbar$, as is often quoted in the literature. We workin isotropic coordinates where the wave equations have a simple managable formand do not make a weak gravitational field approximation. We interpret thesewave equations in terms of a quantum mechanical particle moving in medium witha spatially varying effective index of refraction. Due to the first orderspatial derivative structure of the Dirac equation in curved spacetime, onlythe spin 1/2 particle has \textit{exactly} the quantum mechanical phase asindicated above. The second order spatial derivative structure of the spin 0and spin 1 wave equations yield the above phase only to lowest order in$\hbar$. We develop a WKB approximation for the solution of the spin 0 and spin1 wave equations and explore amplitude and phase corrections beyond the lowestorder in $\hbar$. For the spin 1/2 particle we calculate the phase appropriatefor neutrino flavor oscillations.Comment: 30 pages, no figures. Submitted to Gen.Rel.Grav 17 Oct 0

The Phase of a Quantum Mechanical Particle in Curved Spacetime