Expansion methods for the Dirac equation

Abstract

The applicability of expansion methods to the solution of the Dirac equation is investigated. Criteria are given to distinguish between acceptable and spurious solutions. A careful analysis of the computed eigenvalues as functions of the nonlinear parameters characterizing the basis functions is presented. A definition is given for the measure of the error of the wave function which is calculated by a variational method based on a minimum principle. Illustrative numerical calculations are presented for the one‐particle Dirac equation involving Coulomb and modified Coulomb potentials.