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

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arXiv · 1411.4895

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

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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 $D\geq 4$.

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F. Caruso, J. Martins, L. D. Perlingeiro, V. Oguri. 2014-11-18. Does Dirac equation for a generalized Coulomb-like potential in D+1 dimensional flat spacetime admit any solution for $D\geq 4$?. https://doi.org/10.1016/j.aop.2015.04.009

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