Approximate analytical solutions of the Klein–Gordon equation with the Pöschl–Teller potential including the centrifugal term

Abstract

By employing a new improved approximation scheme to deal with the centrifugal term, we solve approximately the Klein–Gordon equation with scalar and vector 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 basic concept of the supersymmetric shape invariance formalism and the function analysis method. We also discuss in detail the identity of the energy spectra for the Pöschl–Teller potential in the Klein–Gordon equation and the Dirac equation under the limits of the spin symmetry and pseudospin spin symmetry.