  Beginning with Bekenstein, many authors have considered a uniformly spaced
discrete quantum spectrum for black hole horizon area. It is also believed that
the huge degeneracy of these area levels corresponds to the notion of black
hole entropy. Starting from these two assumptions we here infer the algebra of
a Schwarzschild black hole's observables. This algebra then serves as
motivation for introducing in the system's Hamiltonian an interaction term. The
interaction contains the horizon area operator, which is a number operator, and
its canonical conjugate, the phase operator. The Hawking radiation from a
Schwarzschild black hole is seen to be a consequence of an area-phase
interaction. Using this interaction we have reproduced the semi-classical
result for the Hawking radiation power. Furthermore, we show that the initial
state of the black hole determines the nature of its development. Thus, a state
which is an area eigenstate describes a static eternal black hole, but a
coherent state describes a radiating black hole. Hence, it is the observer's
initial knowledge or uncertainty about the horizon area which determines the
evolution.
