Abstract
An efficient numerical method is developed to solve the relativistic hydrogenic Coulomb problem. Combining a pseudospectral method and a change of coordinates, a matrix representation of the relativistic Hamiltonian is constructed in position space. The radial coordinate is mapped from the semi-infinite r-axis to a finite range. The accuracy of the calculation is tested by comparing eigenvalues, sum rules and eigenfunctions with known analytic results. The method can be applied to central field problems for which analytic solutions are unknown.
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