Does Dirac equation for a generalized Coulomb-like potential in D+1 dimensional flat space–time admit any solution for D≥4?

The relativistic hydrogen atom in a 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 th...

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Bibliographic Details
Published in:Annals of physics 2015-08, Vol.359, p.73-79
Main Authors: Caruso, F., Martins, J., Perlingeiro, L.D., Oguri, V.
Format: Article
Language:English
Subjects:
Coulombian potential
Dimensionality
Dirac equation
Hydrogen atom
Space
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Summary:The relativistic hydrogen atom in a 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≥4.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2015.04.009