  The purpose of this paper is to analyse the back reaction problem, between
Hawking radiation and the black hole, in a simplified model for the black hole
evaporation in the quantum geometrodynamics context. The idea is to transcribe
the most important characteristics of the Wheeler-DeWitt equation into a
Schr\"odinger's type of equation. Subsequently, we consider Hawking radiation
and black hole quantum states evolution under the influence of a potential that
includes back reaction. Finally, entropy is estimated as a measure of the
entanglement between the black hole and Hawking radiation states in this model.
