Calculation of Relativistic Single-Particle States
- URL: http://arxiv.org/abs/2312.02500v1
- Date: Tue, 5 Dec 2023 05:07:09 GMT
- Title: Calculation of Relativistic Single-Particle States
- Authors: D. Wingard, B. K\'onya and Z.Papp
- Abstract summary: Method is an extension of a non-relativistic one, where the potential is represented in a Coulomb-Sturmian basis.
In the extension to relativistic problems, we cast the Klein-Gordon and Dirac equations into an effective Schr"odinger form.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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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