Dirac equation with a Coulomb plus scalar potential in D + 1 dimensions

We generalize the Dirac equation to D + 1‐dimensional spacetime. The exact solutions of the D ‐dimensional radial equations with a Coulomb plus scalar potential taking the form 1/ r are analytically presented by studying the Tricomi equations. The energies E ( n, l, D ) are exactly presented. The dependences of the energies E ( n, l, D ) on the dimension D are analyzed in some detail. The energies E ( n , 0, D ) first decrease and then increase when increasing dimension D , but the energies E ( n, l, D ) ( l ≠ 0) increase when increasing dimension D . The energies E ( n , 0, D ) are symmetric with respect to D = 1 for D ∈ (0, 2). It is shown that the energies E ( n, l, D ) ( l ≠ 0) are almost independent of the quantum number l for large D and are completely independent of it if the Coulomb potential is equal to the scalar one. The energies E ( n, l, D ) almost overlap for large D . The dependences of the energies E ( n, l, v ) and E ( n, l, s ) on the vector potential parameter v and scalar potential one s are also studied for D = 3. All are found to decrease when these parameters are increased. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005