Approximate analytical solutions of the relativistic equations with the Deng–Fan molecular potential including a Pekeris-type approximation to the (pseudo or) centrifugal term

Abstract

By employing the Pekeris-type (or a new improved approximation) to deal with the (pseudo or) centrifugal term, we solve the Klein–Gordon and Dirac equations with equally mixed scalar and vector Deng–Fan molecular potentials for all values of l (orbital the angular momentum quantum number) and κ (spin–orbit coupling quantum number), respectively. Using the formalism of the Nikiforov–Uvarov method, the approximate analytical bound state energy equations and the associated two-component spinors corresponding to the two relativistic equations are obtained. Also, special cases including the non-relativistic limits of the relativistic equation are obtained.