Angular-radial integrability of Coulomb-like potentials in Dirac equations

Fabbri, Luca; G. Campos, Andre

doi:10.1063/5.0055250

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Angular-radial integrability of Coulomb-like potentials in Dirac equations

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G. Campos, Andre
Division Prof. Dr. Christoph H. Keitel, MPI for Nuclear Physics, Max Planck Society;

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https://pubs.aip.org/aip/jmp/article/62/11/113505/234095/Angular-radial-integrability-of-Coulomb-like
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https://arxiv.org/pdf/2110.10154.pdf
(Preprint)

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Citation

Fabbri, L., & G. Campos, A. (2021). Angular-radial integrability of Coulomb-like potentials in Dirac equations. Journal of Mathematical Physics, 62(11): 113505. doi:10.1063/5.0055250.

Cite as: https://hdl.handle.net/21.11116/0000-000A-3DA4-9

Abstract

We consider the Dirac equation, written in polar formalism, in the
presence of general Coulomb-like potentials, that is, potentials arising
from the time component of the vector potential and depending only on
the radial coordinate, in order to study the conditions of
integrability, given as some specific form for the solution: we find
that the angular dependence can always be integrated, while the radial
dependence is reduced to finding the solution of a Riccati equation so
that it is always possible, at least in principle. We exhibit the known
case of the Coulomb potential and one special generalization as examples
to show the versatility of the method.