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arXiv · 0806.3067

A B-spline Galerkin method for the Dirac equation

Charlotte Froese Fischer·Oleg Zatsarinny
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Abstract

The B-spline Galerkin method is investigated for the simple eigenvalue problem, $y^{\prime\prime} = -λ^2 y$. 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 $κ$. No spurious solutions were found and excellent agreement was obtained for the R-matrix.

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Charlotte Froese Fischer, Oleg Zatsarinny. 2008-06-18. A B-spline Galerkin method for the Dirac equation. https://doi.org/10.1016/j.cpc.2008.12.010

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