Approximate analytical solutions of the Klein-Gordon equation for the Hulthén potential with the position-dependent mass

The Klein-Gordon equation is solved approximately for the Hulthén potential for any angular momentum quantum number ℓ with the position-dependent mass. Solutions are obtained by reducing the Klein-Gordon equation into a Schrödinger-like differential equation using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the wavefunctions. It is found that the results in the case of constant mass are in good agreement with the ones obtained in the literature.