  In a previous work we studied the interior of the Schwarzschild black hole
implementing an effective minimal length, by applying a modification to the
Poisson brackets of the theory. In this work we perform a proper quantization
of such a system. Specifically, we quantize the interior of the Schwarzschild
black hole in two ways: once by using the standard quantum theory, and once by
following a minimal uncertainty approach. Then, we compare the obtained results
from the two approaches. We show that, as expected, the wave function in the
standard approach diverges in the region where classical singularity is located
and the expectation value of the Kretschmann scalar also blows up on this state
in that region. On the other hand, by following a minimal uncertainty
quantization approach, we obtain 5 new and important results as follows. 1) All
the interior states remain well-defined and square-integrable. 2) The
expectation value of the Kretschmann scalar on the states remains finite over
the whole interior region, particularly where used to be the classical
singularity, therefore signaling the resolution of the black hole singularity.
3) A new quantum number is found which plays a crucial role in determining the
convergence of the norm of states, as well as the convergence and finiteness of
the expectation value of the Kretschmann scalar. 4) A minimum for the radius of
the (2-spheres in the) black holes is found 5) By demanding
square-integrability of states in the whole interior region, an exact relation
between the Barbero-Immirzi parameter and the minimal uncertainty scale is
found.
