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

Lyonell Boulton (1) , Nabile Boussaid (2)

1 Department of Mathematics
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

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.

Mots clés: spectral pollution; quadratic projection method; Dirac operator; approximate eigenvalues; Galerkin method

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Lyonell Boulton, Nabile Boussaid. Non-variational computation of the eigenstates of Dirac operators with radially symmetric potentials. 2008. ⟨hal-00308843⟩