  We derive the functional Schrodinger equation for quantum fields in curved
spacetime in the semiclassical limit of quantum geometrodynamics with a
Gaussian incoherent dust acting as a clock field. We perform the semiclassical
limit using a WKB-type expansion of the wave functional in powers of the
squared Planck mass. The functional Schrodinger equation that we obtain
exhibits a functional time derivative that completes the usual definition of
WKB time for curved spacetime, and the usual Schrodinger-type evolution is
recovered in Minkowski spacetime.
