  In this paper we solve for the quantum propagator of a general time dependent
system quadratic in both position and momentum, linearly coupled to an infinite
bath of harmonic oscillators. We work in the regime where the quantum optical
master equation is valid. We map this master equation to a Schroedinger
equation on Super-Hilbert space and utilize Lie Algebraic techniques to solve
for the dynamics in this space. We then map back to the original Hilbert space
to obtain the solution of the quantum dynamics. The Lie Algebraic techniques
used are preferable to the standard Wei-Norman methods in that only coupled
systems of first order ordinary differential equations and purely algebraic
equations need only be solved. We look at two examples.
