Relativistic Approximate Solutions For a Two-Term Potential: Riemann-Type Equation

Abstract

Approximate analytical solutions of a two-term potential are studied for the relativistic wave equations, namely, for the Klein-Gordon and Dirac equations. The results are obtained by solving of a Riemann-type equation whose solution can be written in terms of hypergeometric function F-2(1)(a; b; c; z). The energy eigenvalue equations and the corresponding normalized wave functions are given both for two wave equations. The results for some special cases including the Manning-Rosen potential, the Hulthen potential and the Coulomb potential are also discussed by setting the parameters as required.