On the application of Brillouin-Wigner perturbation theory to a relativistic and non-relativistic hydrogenic model problem

Abstract

The application of Brillouin-Wigner perturbation theory to a hydrogenic model problem is described using both a relativistic and a nonrelativistic formalism. The nonrelativistic study is carried out by employing a basis set of Coulomb Sturmian functions whereas calculations within the relativistic formalism use basis sets of L-spinors. A two-state hydrogenic model problem provides a dramatic example of the dependence of the convergence behaviour of both the Brillouin-Wigner and the Rayleigh-Schrödinger perturbation expansions on the choice of basic set. Two types of Brillouin-Wigner perturbation expansion are compared in both the relativistic and the nonrelativistic formulations, the first u..