The time-dependent quantum Hamiltonians $$\hat H\left( t \right) = \left\{ {\begin{array}{*{20}c} {\hat H,t_i|n0>, where |e> is the excited state of the two-level atom and $$\left. {\left. {\hat N} \right|n_0 } \right\rangle = \left. {\left. {n_0 } \right|n_0 } \right\rangle $$ . Using a suitable loop algebra, we derive a Lax pair formulation of the operator equations of motion during the times t int for any N. For N=2 and N=3, the nonlinear operator equations linearize under appropriate additional nonlinear conditions; we obtain operator solutions for N=2 and N=3. We then give the N=2 masing solution. Having investigated the semiclassical limits of the nonlinear operator equations of motion, we conclude that “quantum chaos’ cannot be created in an N-atom micromaser for any value of N. One difficulty is the proper form of the semiclassical limits for the N-atom operator problems. Because these c-number semiclassical forms have an unstable singular point, “quantum chaos” might be created by driving the real quantum system with an additional external microwave field coupled to the maser cavity.