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

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...

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Bibliographic Details
Published in:arXiv.org 2015-04
Main Authors: Caruso, F, Martins, J, Perlingeiro, L D, Oguri, V
Format: Article
Language:English
Subjects:
Dirac equation
Euclidean geometry
Euclidean space
Online Access:Get full text
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Summary: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 \(D\geq 4\).
ISSN:2331-8422
DOI:10.48550/arxiv.1411.4895