  We present a quantum jump approach to describe coupled quantum and classical
systems in the context of Bose-Einstein condensation in the solid state. In our
formalism, the excitonic gain medium is described by classical rate equations,
while the polariton modes are described fully quantum mechanically. We show the
equivalence of our method with a master equation approach. As an application,
we compute the linewidth of a single mode polariton condensate. Both the line
broadening due to the interactions between polaritons and the interactions with
the reservoir excitons is taken into account.
