  The functional Schrodinger equation is used to study the quantum collapse of
a gravitating, spherical domain wall and a massless scalar field coupled to the
metric. The approach includes backreaction of pre-Hawking radiation on the
gravitational collapse. Truncating the degrees of freedom to a minisuperspace
leads to an integro-differential Schrodinger equation. We define a "black hole"
operator and find its eigenstates. The black hole operator does not commute
with the Hamiltonian, leading to an energy-black holeness uncertainty relation.
We discuss energy eigenstates and also obtain a partial differential equation
for the time-dependent gravitational collapse problem.
