On the Solution of the Generalized Symmetric Woods-Saxon Potential in the Dirac Equation

Abstract

In this work, we present a solution to the Diracequation that is coupled with vector and scalar generalized symmetricWoods-Saxon potential energy in one plus one space-time.  The chosen potential energy has a flexiblestructure to examine four different physical problems. The potential energy canbe a barrier or well depend on being attractive or repulsive. Furthermore, theincluded surface effects can be attractive or repulsive. Therefore, in oneclass a potential barrier occurs with a pocket or an extra barrier nearby theeffective radius. Similar effects occur in the potential well whether thesurface effects are repulsive or attractive. Here we use the usualtwo-component approach. We obtain the solutions in hypergeometric functionform.