A B-spline Galerkin method for the Dirac equation

Abstract

The B-spline Galerkin method is investigated for the simple eigenvalue problem, $y^{\prime \prime }=-{\lambda }^{2}y$. Special attention is give to boundary conditions. From this analysis, we propose a stable method for the Dirac equation and evaluate its accuracy by comparing the computed and exact R-matrix for a wide range of nuclear charges $Z$ and angular quantum numbers $\kappa$. No spurious solutions were found and excellent agreement was obtained for the R-matrix.

PDFTex, 5 pages and 4 figures

References in corpus (1)

• Application of the dual-kinetic-balance sets in the relativistic many-body problem of atomic structure

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