On the analysis of the Eigenvalues of the Dirac equation with A 1/r potential in D dimensions

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 DeltaE(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) (I not equal 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, xi) on the potential strength are also studied for the given dimension D = 3. We find that the energies E(n, l, xi) decrease with xi less than or equal to l + 1.