Iterative solutions to the Dirac equation

Abstract

We consider a single particle which is bound by a central potential and obeys the Dirac equation in $d$ dimensions. We first apply the asymptotic iteration method to recover the known exact solutions for the pure Coulomb case. For a screened Coulomb potential and for a Coulomb plus linear potential with linear scalar confinement, the method is used to obtain accurate approximate solutions for both eigenvalues and wave functions.