  We consider a Hamiltonian theory of spherically symmetric vacuum Einstein
gravity under Kruskal-like boundary conditions in variables associated with the
Einstein-Rosen wormhole throat. The configuration variable in the reduced
classical theory is the radius of the throat, in a foliation that is frozen at
the left hand side infinity but asymptotically Minkowski at the right hand side
infinity, and such that the proper time at the throat agrees with the right
hand side Minkowski time. The classical Hamiltonian is numerically equal to the
Schwarzschild mass. Within a class of Hamiltonian quantizations, we show that
the spectrum of the Hamiltonian operator is discrete and bounded below, and can
be made positive definite. The large eigenvalues behave asymptotically
as~$\sqrt{2k}$, where $k$ is an integer. The resulting area spectrum agrees
with that proposed by Bekenstein and others. Analogous results hold in the
presence of a negative cosmological constant and electric charge. The classical
input that led to the quantum results is discussed.
