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

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 $D\ge 4$.

12 pages, 1 figure, 1 table

References in corpus (2)

• Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss' law
• Numerov numerical method applied to the Schrödinger equation

Cited by in corpus (1)

• Still learning about space dimensionality: from the description of hydrogen atom by a generalized wave equation for dimensions D$\ge$3