Perturbation theory and the two-level approximation: A corollary and critique

► Implications of using the two-level model in nonlinear optics. ► Theorem on the expectation values for functions of quantum operators. ► Relevance for the design criteria of 'push-pull' optical materials. ► Paradoxical results of two-level calculations resolved. ► Pitfalls in using perturbation theory with a two-level model.