Angular-Radial Integrability of Coulomb-like Potentials in Dirac Equations
arXiv:2110.10154 · doi:10.1063/5.0055250
Abstract
We consider the Dirac equation, written in polar formalism, in 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.
arXiv comment8 pages. arXiv admin note: text overlap with arXiv:2003.10825
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