  The wavefunctional in quantum gravity gives an amplitude for 3-geometries and
matter fields. The four-space is usually recovered in a semiclassical
approximation where the gravity variables are taken to oscillate rapidly
compared to matter variables; this recovers the Schrodinger evolution for the
matter. We examine turning points in the gravity variables where this
approximation appears to be troublesome. We investigate the effect of such a
turning point on the matter wavefunction, in simple quantum mechanical models
and in a closed minisuperspace cosmology. We find that after evolving
sufficiently far from the turning point the matter wavefunction recovers to a
form close to that predicted by the semiclassical approximation, and we compute
the leading correction (from `backreaction') in a simple model. We also show
how turning points can appear in the gravitational sector in dilaton gravity.
We give some remarks on the behavior of the wavefunctional in the vicinity of
turning points in the context of dilaton gravity black holes.
