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arXiv · 2312.02500

Calculation of Relativistic Single-Particle States

D. Wingard·B. Kónya·Z. Papp
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Abstract

A computational method is proposed to calculate bound and resonant states by solving the Klein-Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential is represented in a Coulomb-Sturmian basis. This basis facilitates the exact analytic evaluation of the Coulomb Green's operator in terms of a continued fraction. In the extension to relativistic problems, we cast the Klein-Gordon and Dirac equations into an effective Schr\"odinger form. Then the solution method is basically an analytic continuation of non-relativistic quantities like the angular momentum, charge, energy and potential into the effective relativistic counterparts.

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D. Wingard, B. Kónya, Z. Papp. 2023-12-05. Calculation of Relativistic Single-Particle States. https://doi.org/10.1007/s00601-023-01869-y

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