ON THE ANALYSIS OF THE EIGENVALUES OF THE DIRAC EQUATION WITH A 1/r POTENTIAL IN D DIMENSIONS

Abstract

The Dirac equation is investigated in D+1 dimensional space-time. The radial equations of this quantum system are obtained and solved exactly by the confluent hypergeometric equation approach. The energy levels E(n,l,D) are analytically presented. For the continuous dimension D as proposed by Nieto, the dependences of the energy difference ΔE(n,l,D) for D and D-1 on the dimension D are demonstrated as three different kinds of change rules. The dependences of the energy E(n,l,D) on the dimension D are also discussed. It is found that the energies E(n,l,D) (l≠0) are almost independent of the quantum number l for a large D, while E(n,0,D) first decreases and then increases with the increasing dimension D. The dependences of the energies E(n,l,ξ) on the potential strength ξ are also studied for the given dimension D=3. We find that the energies E(n,l,ξ) decrease with ξ≤l+1.