Effective Hamiltonians, two-level systems, and generalized Maxwell-Bloch equations

A new method is proposed which involves a canonical transformation leading to the nonsecular part of time-independent perturbation calculus. The method is used to derive expressions for effective Shen-Walls Hamiltonians which, taken in the two-level approximation and on the inclusion of non-Hamiltonian terms into the dynamics of the system, lead to generalized Maxwell-Bloch equations. The rotating-wave approximation is written anew within the framework of our formalism.