Improvement of the Basis for the Solution of the Dirac Equation in Cassini Coordinates
Atomic Physics
2017-08-30 v3 Quantum Physics
Abstract
We propose an improvement of the basis for the solution of the stationary two-centre Dirac equation in Cassini coordinates using the finite-basis-set method presented in Ref. [1]. For the calculations in Ref. [1], we constructed the basis for approximating the energy eigenfunctions by using smooth piecewise defined polynomials, called B-splines. In the present article, we report that an analysis of the employed representation of the Dirac matrices shows that the above approximation is not efficient using B-splines only. Therefore, we include basis functions which are defined using functions with step-like behaviour instead of B-splines. Thereby, we achieve a significant increase of accuracy of results as compared to Ref. [1].
Keywords
Cite
@article{arxiv.1610.05263,
title = {Improvement of the Basis for the Solution of the Dirac Equation in Cassini Coordinates},
author = {Walter Hahn and Anton N. Artemyev and Andrey Surzhykov},
journal= {arXiv preprint arXiv:1610.05263},
year = {2017}
}