Solutions of the radial Dirac equation in a B-polynomial basis

Abstract

An algorithm is given for constructing accurate solutions to the radial Dirac equation in a B-polynomial basis set. The B-polynomial Galerkin method has been applied to produce the spectrum of the Dirac equation for the bound states of hydrogenic systems. Matrix formulation is used throughout the entire procedure and boundary conditions are applied to generate finite discrete eigenvalues, which include both negative and positive energies as well as corresponding states. An excellent agreement is found between previously existing accurate calculations. To check the quality of the spectrum, the resulting basis sets are used to evaluate the TRK sum rules. The procedure can be readily extended to produce the spectrum of complex systems.