  We consider a Hamiltonian quantum theory of spherically symmetric,
asymptotically flat electrovacuum spacetimes. The physical phase space of such
spacetimes is spanned by the mass and the charge parameters $M$ and $Q$ of the
Reissner-Nordstr\"{o}m black hole, together with the corresponding canonical
momenta. In this four-dimensional phase space, we perform a canonical
transformation such that the resulting configuration variables describe the
dynamical properties of Reissner-Nordstr\"{o}m 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 ADM mass of the hole, from the
point of view of a distant observer at rest, is obtained. Our eigenvalue
equation implies that the ADM mass and the electric charge spectra of the hole
are discrete, and the mass spectrum is bounded below. Moreover, the spectrum of
the quantity $M^2-Q^2$ is strictly positive when an appropriate self-adjoint
extension is chosen. The WKB analysis yields the result that the large
eigenvalues of the quantity $\sqrt{M^2-Q^2}$ 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.
