Inst High Energy Phys, Beijing 100039, Peoples R China
; Univ Nacl Autonoma Mexico, Inst Ciencias Nucl, Mexico City 04510, DF, Mexico
; Inst Mexicano Petr, Programa Ingn Mol, Mexico City 07730, DF, Mexico
The solutions of the Klein-Gordon equation with a Coulomb potential in D dimensions are obtained exactly, and the energy levels E (n, l, D) are analytically presented. The dependence of the energy difference DeltaE(n, l, D) for D and D - 1 on the dimension D is demonstrated as three different kinds of rules. The dependence of the energy E(n, l, D) on the dimension D is also analyzed. It is shown that the energy E(n, l, D) (l not equal 0) is almost independent of the quantum number 1, while E(n, 0, D) first decreases and then increases as the dimension D increases. There is no bound state of the S-wave for D = 2.