Bound state solutions of the Klein–Gordon equation with the generalized Pöschl–Teller potential

By employing an improved new approximation scheme to deal with the centrifugal term, we solve approximately the Klein–Gordon equation with equal scalar and vector generalized Pöschl–Teller potentials for the arbitrary orbital angular momentum number l . The bound state energy equation and the unnormalized radial wave functions have been approximately obtained by using the supersymmetric shape invariance approach and the function analysis method. It is found that the present approximate analytical results are in better agreement with those obtained by using the numerical integration approach for small values of α than the approximate results obtained by using the conventional approximation to the centrifugal term.