  A solvable 2-dimensional conformally invariant midi-superspace model for
black holes is obtained by imposing spherical symmetry in 4-dimensional
conformally invariant Einstein gravity. The Wheeler-DeWitt equation for the
theory is solved exactly to obtain the unique quantum wave functional for an
isolated black hole with fixed mass. By suitably relaxing the boundary
conditions, a non-perturbative ansatz is obtained for the wave functional of a
black hole interacting with its surroundings.
