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We consider a quantum mechanical black hole model introduced in {\itPhys.Rev.}, {\bf D57}, 1118 (1998) that consists of the selfgravitating dustshell. The Schroedinger equation for this model is a finite difference equationwith the shift of the argument along the imaginary axis. Solving this equationin quasiclassical limit in complex domain leads to quantization conditions thatdefine discrete quasiclassical mass spectrum. One of the quantizationconditions is Bohr-Sommerfeld condition for the bound motion of the shell. Theother comes from the requirement that the wave function is unambiguouslydefined on the Riemannian surface on which the coefficients of Schroedingerequation are regular. The second quantization condition remains valid for theunbound motion of the shell as well, and in the case of a collapsing null-dustshell leads to $m\sim\sqrt{k}$ spectrum.Comment: 35 pages, 8 figures, to appear in Phys. Rev.

Quasiclassical mass spectrum of the black hole model with a self-gravitating dust shell