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

This analysis addresses the use of a two-level approximation to simplify expressions derived from perturbation theory. It is shown that the limitations of validity for the emergent results are more stringent than is commonly understood, being equivalent in effect to the adoption of a more extensive approximation – one that significantly undermines the perturbative origin of those expressions. Effectively truncating the completeness relation, a series of interconnected operator relations comes into play, some with physically untenable consequences. A new theorem on the expectation values of operator functions highlights additional constraints upon any molecule modelled as a two-level system.