  In this paper, we study the matrix model proposed by Berenstein, Maldacena,
and Nastase to describe M-theory on the maximally supersymmetric pp-wave. We
show that the model may be derived directly as a discretized theory of
supermembranes in the pp-wave background, or alternatively, from the dynamics
of D0-branes in type IIA string theory. We consider expanding the model about
each of its classical supersymmetric vacua and note that for large values of
the mass parameter \mu, interaction terms are suppressed by powers of 1/mu, so
that the model may be studied in perturbation theory. We compute the exact
spectrum about each of the vacua in the large \mu limit and find the complete
(infinite) set of BPS states, which includes states preserving 2, 4, 6, 8, or
16 supercharges. Through explicit perturbative calculations, we then determine
the effective coupling that controls the perturbation expansion for large \mu
and estimate the range of parameters and energies for which perturbation theory
is valid.
