Spurious Modes in Dirac Calculations and How to Avoid Them

  • Mathieu LewinEmail author
  • Éric Séré
Part of the Mathematical Physics Studies book series (MPST)


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.


Dirac Operator Coulomb Potential Lower Spinor Essential Spectrum Spinor Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



M. L. would like to thank Lyonell Boulton and Nabile Boussaid for stimulating discussions, in particular concerning the numerical experiments of this article. M. L. has received financial support from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement MNIQS 258023). M. L. and É. S. acknowledge financial support from the French Ministry of Research (ANR-10-BLAN-0101).


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Département de Mathématiques (CNRS UMR 8088)Université de Cergy-PontoiseCergy-Pontoise CedexFrance
  2. 2.Ceremade (CNRS UMR 7534)Université Paris-Dauphine, Place de Lattre de TassignyParis Cedex 16France

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