  Quantum stochastic operator equations are derived for inter-branch exciton
and polariton processes caused by acoustic phonon scattering. The use of a
fully quantum model combined with these recently developed techniques predicts
the presence of ``stimulated scattering'' terms, and provides a sound basis for
understanding the basis of the approximations used in generating the equations.
The theory is applied to a model motivated by recent experiments where a
stronger photoluminescence signal from the high energy microcavity polariton
polariton is observed for low excitation powers, and also to an experimental
scheme designed to show evidence of the stimulated scattering effect.
