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 Schrödinger 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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Wingard, D., Kónya, B. & Papp, Z. Calculation of Relativistic Single-Particle States. Few-Body Syst 64, 88 (2023). https://doi.org/10.1007/s00601-023-01869-y
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DOI: https://doi.org/10.1007/s00601-023-01869-y