  The quantum black hole model with a self-gravitating spherically symmetric
thin dust shell as a source is considered. The shell Hamiltonian constraint is
written and the corresponding Schroedinger equation is obtained. This equation
appeared to be a finite differences equation. Its solutions are required to be
analytic functions on the relevant Riemannian surface. The method of finding
discrete spectra is suggested based on the analytic properties of the
solutions. The large black hole approximation is considered and the discrete
spectra for bound states of quantum black holes and wormholes are found. They
depend on two quantum numbers and are, in fact, quasi-continuous. The quantum
black hole bound state depends not only on mass but also on an additional
quantum number, and black holes with the same mass have different quantum
hairs. These hairs exhibit themselves at the Planckian distances near the black
hole horizon. For the observer who can not measure the distances smaller than
the Planckian length the black hole has the only parameter, its mass. The
other, non-measurable, parameter leads to the quantum corrections to the black
hole entropy. The quantum states with given mass are the mixed ones. It is
shown that there exists the ground quantum black hole state with minimal mass
equal approximately the Planckian mass. Its quantum state has zero entropy and
it is a pure state. The existence of the quantum hairs may solve (at least
partially) the well known information paradox in the black hole physics.
