Another method to solve Dirac's one-electron equation numerically

TL;DR

This paper introduces a new numerical method for solving Dirac's one-electron equation that effectively avoids spurious states and can accurately compute highly excited states for spherically symmetric potentials.

Contribution

A novel numerical approach for the Dirac equation that eliminates spurious solutions and enhances precision for excited states in spherically symmetric potentials.

Findings

Method is free of spurious states for Coulomb potential.

Can accurately compute highly excited states.

Applicable to spherically symmetric bound potentials.

Abstract

One more mode developed to get eigen energies and states for the one-electron Dirac's equation with spherically symmetric bound potential. For the particular case of the Coulomb potential it was shown that the method is free of so called spurious states. The procedure could be adapted to receive highly exited states with great precision.