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

Part of: Special classes of linear operators Quantum theory

Published online by Cambridge University Press:  01 January 2010

Lyonell Boulton  and
Nabile Boussaid
Lyonell Boulton
Affiliation:
Ceremade (UMR CNRS 7534) Université Paris-Dauphine, Place de Lattre de Tassigny, F-75775 Paris Cedex 16, France Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom (email: L.Boulton@hw.ac.uk)
Nabile Boussaid
Affiliation:
Département de Mathématiques, UFR Sciences et techniques, 16 route de Gray - 25 030, Besançon Cedex, France (email: nabile.boussaid@univ-fcomte.fr)

Abstract

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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 in the fact that it avoids completely the phenomenon of spectral pollution and it always provides two-sided estimates for the eigenvalues with explicit error bounds on both eigenvalues and eigenfunctions. We also discuss convergence rates of the method and illustrate our results with various numerical experiments.

MSC classification

Secondary: 47B36: Jacobi (tridiagonal) operators (matrices) and generalizations 47B39: Difference operators 81-08: Computational methods

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 13 , January 2010 , pp. 10 - 32
Copyright
Copyright © London Mathematical Society 2010

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