Spurious Modes in Dirac Calculations and How to Avoid Them

Abstract

In this paper we consider the problem of the occurrence of spurious modes when computing the eigenvalues of Dirac operators, with the motivation to describe relativistic electrons in an atom or a molecule. We present recent mathematical results which we illustrate by simple numerical experiments. We also discuss open problems.

Chapter to be published in the book "Many-Electron Approaches in Physics, Chemistry and Mathematics: A Multidisciplinary View", edited by Volker Bach and Luigi Delle Site

References in corpus (1)

• On the eigenvalues of operators with gaps. Application to Dirac operators

Cited by in corpus (3)

• Extending the class of solutions of the Dirac equation using tridiagonal matrix representations
• Analytical evaluation of relativistic molecular integrals. II. Computational aspect for relativistic molecular auxiliary functions
• Analytical solutions of the Dirac equation using the Tridiagonal Representation Approach: General study, limitations, and possible applications