Expansion methods for the Dirac equation

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.