Perturbation theory by the moment method and point-group symmetry

TL;DR

This paper examines the use of the moment method in perturbation theory for anharmonic oscillators, highlighting the role of point-group symmetry in predicting suitable states for correction calculations.

Contribution

It clarifies the application of symmetry considerations in the moment method for perturbation theory, improving the accuracy of excited state calculations.

Findings

Symmetry analysis predicts which states need special treatment.

Some earlier methods were unsuitable for certain excited states.

Point-group symmetry aids in selecting correct perturbation corrections.

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 $C_{4v}$ and $C_{2v}$ 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.