Bound states of the Klein-Gordon equation in D-dimensions with some physical scalar and vector exponential-type potentials including orbital centrifugal term

Abstract

The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital angular momentum number l and dimensional space D. The relativistic/non-relativistic energy spectrum equation and the corresponding unnormalized radial wave functions, in terms of the Jacobi polynomials P_{n}^{({\alpha},{\beta})}(z), where {\alpha}>-1, {\beta}>-1 and z\in[-1,+1] or the generalized hypergeometric functions _{2}F_{1}(a,b;c;z), are found. The Nikiforov-Uvarov (NU) method is used in the solution. The solutions of the Eckart, Rosen-Morse, Hulth\'en and Woods-Saxon potential models can be easily obtained from these solutions. Our results are identical with those ones appearing in the literature. Finally, under the PT-symmetry, we can easily obtain the bound state solutions of the trigonometric Rosen-Morse potential.