Eigenfunction method for splitting of energy levels in quantum mechanics

Abstract

In this work, we illustrate the use of eigenfunction method (EFM) in quantum mechanics by taking a specific example namely the splitting of energy levels under perturbation. Initially, the symmetry group of the Hamiltonian is taken to be [Formula: see text] which under the action of a perturbing potential changes to a lower symmetry namely [Formula: see text]. We have constructed an irreducible basis using the EFM for both the symmetries and show the simplifications that ensure the calculation of the expectation value of the perturbing Hamiltonian.