  We study some quantum mechanical aspects of dynamical black holes where the
Vaidya metric is used as a model representing evaporating black holes. It is
shown that in this model the Wheeler-DeWitt equation is solvable in whole
region of spacetime, provided that one considers the ingoing (or outgoing)
Vaidya metric and selects a suitable coordinate frame. This wave function has
curious features in that near the curvature singularity it oscillates violently
owing to large quantum effects while in the other regions the wave function
exhibits a rather benign and completely regular behavior. The general formula
concerning the black hole radiation, which reduces to the Hawking's
semiclassical result when $r = 2M$ is chosen, is derived by means of purely
quantum mechanical approach. The present formulation can be applied essentially
to any system with a spherically symmetric black hole in an arbitrary spacetime
dimension.
