Perturbation theory by the moment method and point-group symmetry

Abstract

We analyze earlier applications of perturbation theory by the moment method (also called inner product method) to anharmonic oscillators. For concreteness we focus on two-dimensional models with symmetry (Formula presented.) and (Formula presented.) and reveal the reason why some of those earlier treatments proved unsuitable for the calculation of the perturbation corrections for some excited states. Point-group symmetry enables one to predict which states require special treatment.