  Nathan Rosen's quantization approach to the gravitational collapse is applied
in the simple case of a pressureless "star of dust" by finding the
gravitational potential, the Schrodinger equation and the solution for the
collapse's energy levels. By applying the constraints for a Schwarzschild black
hole (BH) and by using the concept of BH effective state, previously introduced
by one of the authors (CC), the BH quantum gravitational potential, Schrodinger
equation and the BH energy spectrum are found. Remarkably, such an energy
spectrum is in agreement (in its absolute value) with the one which was
conjectured by Bekenstein in 1974 and consistent with other ones in the
literature. This approach also permits to find an interesting quantum
representation of the Schwarzschild BH ground state at the Planck scale.
Moreover, two fundamental issues about BH quantum physics are addressed by this
model: the area quantization and the singularity resolution. As regards the
former, a result similar to the one obtained by Bekenstein, but with a
different coefficient, has been found. About the latter, it is shown that the
traditional classical singularity in the core of the Schwarzschild BH is
replaced, in a full quantum treatment, by a two-particle system where the two
components strongly interact with each other via a quantum gravitational
potential. The two-particle system seems to be non-singular from the quantum
point of view and is analogous to the hydrogen atom because it consists of a
"nucleus" and an "electron".
