  We consider a Hamiltonian quantum theory of stationary spacetimes containing
a Kerr-Newman black hole. The physical phase space of such spacetimes is just
six-dimensional, and it is spanned by the mass $M$, the electric charge $Q$ and
angular momentum $J$ of the hole, together with the corresponding canonical
momenta. In this six-dimensional phase space we perform a canonical
transformation such that the resulting configuration variables describe the
dynamical properties of Kerr-Newman black holes in a natural manner. The
classical Hamiltonian written in terms of these variables and their conjugate
momenta is replaced by the corresponding self-adjoint Hamiltonian operator and
an eigenvalue equation for the Arnowitt-Deser-Misner (ADM) mass of the hole,
from the point of view of a distant observer at rest, is obtained. In a certain
very restricted sense, this eigenvalue equation may be viewed as a sort of
"Schr\"odinger equation of black holes". Our "Schr\"odinger equation" implies
that the ADM mass, electric charge and angular momentum spectra of black holes
are discrete, and the mass spectrum is bounded from below. Moreover, the
spectrum of the quantity $M^2-Q^2-a^2$, where $a$ is the angular momentum per
unit mass of the hole, is strictly positive when an appropriate self-adjoint
extension is chosen. The WKB analysis yields the result that the large
eigenvalues of $M$, $Q$ and $a$ are of the form $\sqrt{2n}$, where $n$ is an
integer. It turns out that this result is closely related to Bekenstein's
proposal on the discrete horizon area spectrum of black holes.
