Non-variational computation of the eigenstates of Dirac operators with radially symmetric potentials

TL;DR

This paper introduces a new computational method for Dirac operators with radial potentials that avoids spectral pollution, provides reliable eigenvalue estimates with explicit error bounds, and demonstrates convergence through numerical experiments.

Contribution

The paper presents a novel strategy for eigenvalue computation of Dirac operators that guarantees two-sided estimates and explicit error bounds, improving accuracy and reliability.

Findings

Method avoids spectral pollution.

Provides explicit error bounds for eigenvalues and eigenfunctions.

Demonstrates convergence through numerical experiments.

Abstract

We discuss a novel strategy for computing the eigenvalues and eigenfunctions of the relativistic Dirac operator with a radially symmetric potential. The virtues of this strategy lie on the fact that it avoids completely the phenomenon of spectral pollution and it always provides two-side estimates for the eigenvalues with explicit error bounds on both eigenvalues and eigenfunctions. We also discuss convergence rates of the method as well as illustrate our results with various numerical experiments.