Unification of Phase-Space Descriptions of Quantum Markovian Systems

We describe a general approach for the analysis of "phase-space" or "$c$-number" descriptions of complex quantum systems. Our approach is similar to that recently developed by Agarwal and Wolf, but is based upon a formalism developed by Lax. We show that the $c$-number description of atomic operator equations employed by Gordon in his theory of the laser can be derived from an operator ordering formalism. A general method for deriving a Fokker-Planck equation in any $c$-number association scheme from a given Markovian operator equation is shown. The formalism is employed to find expressions for arbitrary multitime averages in terms of two-time conditional probabilities alone.