Iterative solution of a Dirac equation with inverse Hamiltonian method

TL;DR

This paper introduces an iterative inverse Hamiltonian method to solve the Dirac equation in coordinate space, effectively avoiding variational collapse and accurately reproducing solutions.

Contribution

It presents a novel iterative approach that maximizes the inverse Hamiltonian expectation to solve the Dirac equation without collapse.

Findings

Method efficiently reproduces exact Dirac solutions

Avoids variational collapse in iterative solutions

Works well with Woods-Saxon potentials

Abstract

We solve a singe-particle Dirac equation with Woods-Saxon potentials using an iterative method in the coordinate space representation. By maximizing the expectation value of the inverse of the Dirac Hamiltonian, this method avoids the variational collapse, in which an iterative solution dives into the Dirac sea. We demonstrate that this method works efficiently, reproducing the exact solutions of the Dirac equation.