Approximate analytical solutions of the Dirac equation with the generalized Pöschl–Teller potential including the pseudo-centrifugal term

By employing an improved approximation scheme to deal with the pseudo-centrifugal term, we solve approximately the Dirac equation with the generalized Pöschl–Teller potential for the arbitrary spin–orbit quantum number κ. Under the condition of pseudospin symmetry, the bound state energy eigenvalues and the associated two-component spinors of the Dirac particle are obtained approximately by using the basic concept of the supersymmetric shape invariance formalism and the function analysis method.