We quantize by the Dirac-Wheeler-DeWitt method the canonical formulati
on of the Schwarzschild black hole developed in a previous paper. We i
nvestigate the properties of the operators that generate rigid symmetr
ies of the Hamiltonian, establish the form of the invariant measure un
der the rigid transformations, and determine the gauge fixed Hilbert s
pace of states. We also prove that the reduced quantization method lea
ds to the same Hilbert space for a suitable gauge fixing.