Bound state solutions of the Klein-Gordon equation with position-dependent mass for the inversely linear potential

In this paper we study the problem of the relativistic motion of a spin-zero particle in one dimension where the potential energy and mass are inversely proportional to the distance from the force center. Bound state solutions of the Klein-Gordon equation with position-dependent mass for the inversely linear potential were obtained by using the Nikiforov-Uvarov method. The energy spectra of the Klein-Gordon equation are discussed for the case when the scalar and vector potentials are equal in both sign and magnitude and for the case when they are equal in magnitude but not in sign.