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Mini-workshop on "Numerical challenges in relativistic quantum mechanics"
Organizers: Werner Kutzelnigg (Bochum), Eric Séré (Paris-Dauphine)

Mathieu Lewin (CNRS & Cergy-Pontoise, France): "Spectral pollution in relativistic calculations based on the Dirac operator"
Friday 19 April 2013, 14:00 - 14:45
Amphi Hermite

Mathieu LEWIN
CNRS and Université de Cergy-Pontoise, France

It is well known that computing the eigenvalues of a Dirac operator can lead to spurious solutions. This phenomenon was for instance observed for the hydrogen atom by Drake and Goldman in 1981. Several methods to avoid this phenomenon have been proposed in the physics and chemistry literature. The most celebrated of them is the so-called "kinetic balance method". In this talk I will present a rigorous analysis of these techniques. In particular, I will explain that the kinetic balance method is guaranteed to work for smooth electric potentials, but not for Coulomb potentials. Joint work with Eric Séré.

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