Does Dirac equation for a generalized Coulomb-like potential in D+1 dimensional flat spacetime admit any solution for $D\geq 4$?

F. Caruso; J. Martins; L. D. Perlingeiro; V. Oguri

doi:10.1016/j.aop.2015.04.009

Does Dirac equation for a generalized Coulomb-like potential in D+1 dimensional flat spacetime admit any solution for $D\geq 4$?

Quantum Physics 2021-10-19 v2

Authors: F. Caruso , J. Martins , L. D. Perlingeiro , V. Oguri

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Abstract

The relativistic hydrogen atom in an Euclidean space-time of arbitrary number of space dimensions ( $D$ ) plus one time dimension is revisited. In particular, numerical solutions of the radial Dirac equation for a generalized Coulombian potential proportional to $1/r^{(D-2)}$ are investigated. It is argued that one could not find any physical solution for $D\geq 4$ .

Keywords

Dirac equation generalized Coulomb potential D+1 dimensional spacetime relativistic hydrogen atom radial equation numerical solutions physical solution

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@article{arxiv.1411.4895,
  title  = {Does Dirac equation for a generalized Coulomb-like potential in D+1 dimensional flat spacetime admit any solution for $D\geq 4$?},
  author = {F. Caruso and J. Martins and L. D. Perlingeiro and V. Oguri},
  journal= {arXiv preprint arXiv:1411.4895},
  year   = {2021}
}

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12 pages, 1 figure, 1 table

Does Dirac equation for a generalized Coulomb-like potential in D+1 dimensional flat spacetime admit any solution for $D\geq 4$?

Abstract

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