A B-spline Galerkin method for the Dirac equation

Details A B-spline Galerkin method for the Dirac equation A B-spline Galerkin method for the Dirac equation

2008-06-18

arxiv.org/abs/0806.3067v1

Physics

Atomic Physics

PDFTex, 5 pages and 4 figures

Scientific paper

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.

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