Approximate solution of the Dirac equation using the partitioning technique

Abstract

It is shown how the partitioning method of Löwdin may be used to obtain approximate solutions to the Dirac equation. By using a novel separation of the partitioned wave equation perturbation theory may be employed with the solutions of the Schrödinger equation as the zeroth order functions. The method is demonstrated for the 1s, 2s and 2p states of the hydrogen atom and in particular the energies correct to order mc ² α⁶ are obtained. The first and second order contributions to the energy are both finite so the problem of divergences is avoided.