  We investigate the quantum mechanical wave equations for free particles of
spin 0,1/2,1 in the background of an arbitrary static gravitational field in
order 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 work
in isotropic coordinates where the wave equations have a simple managable form
and do not make a weak gravitational field approximation. We interpret these
wave equations in terms of a quantum mechanical particle moving in medium with
a spatially varying effective index of refraction. Due to the first order
spatial derivative structure of the Dirac equation in curved spacetime, only
the spin 1/2 particle has \textit{exactly} the quantum mechanical phase as
indicated above. The second order spatial derivative structure of the spin 0
and 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 spin
1 wave equations and explore amplitude and phase corrections beyond the lowest
order in $\hbar$. For the spin 1/2 particle we calculate the phase appropriate
for neutrino flavor oscillations.
