Iterative solutions to the Dirac equation
Hakan Ciftci, Richard L. Hall, Nasser Saad
TL;DR
This paper applies the asymptotic iteration method to solve the Dirac equation for various potentials, providing exact solutions for Coulomb and approximate solutions for screened-Coulomb and linear confinement potentials.
Contribution
It demonstrates the effectiveness of the asymptotic iteration method in solving the Dirac equation for different potential models, including new approximate solutions.
Findings
Exact solutions for Coulomb potential obtained
Accurate approximate eigenvalues for screened-Coulomb potential
Approximate solutions for Coulomb plus linear potential
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.
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