Quantum black hole model and Hawking’s radiation

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Abstract
The black hole model with a self-gravitating charged spherical symmetric dust thin shell as a source is considered. The Schrödinger-type equation for such a model is derived. This equation appears to be a finite difference equation. A theory of such an equation is developed and a general solution is found and investigated in detail. The discrete spectrum of the bound state energy levels is obtained. All the eigenvalues appear to be infinitely degenerate. The ground state wave functions are evaluated explicitly. The quantum black hole states are selected and investigated. It is shown that the obtained black hole mass spectrum is compatible with the existence of Hawking’s radiation in the limit of low temperature both for large and nearly extreme Reissner-Nordström black holes. The above-mentioned infinite degeneracy of the mass (energy) eigenvalues may appear helpful in resolving the well-known information paradox in black hole physics.
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