  We study the non-linear quantum master equation describing a laser under the
mean field approximation. The quantum system is formed by a single mode optical
cavity and two level atoms, which interact with reservoirs. Namely, we
establish the existence and uniqueness of the regular solution to the
non-linear operator equation under consideration, as well as we get a
probabilistic representation for this solution in terms of a mean field
stochastic Schr\"ondiger equation. To this end, we find a regular solution for
the non-autonomous linear quantum master equation in
Gorini-Kossakowski-Sudarshan-Lindblad form, and we prove the uniqueness of the
solution to the non-autonomous linear adjoint quantum master equation in
Gorini-Kossakowski-Sudarshan-Lindblad form. Moreover, we obtain rigorously the
Maxwell-Bloch equations from the mean field laser equation.
