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Chapitre D'ouvrage Année : 2023

Which Nuclear Shape Generates the Strongest Attraction on a Relativistic Electron? An Open Problem in Relativistic Quantum Mechanics

Résumé

In this article we formulate several conjectures concerning the lowest eigenvalue of a Dirac operator with an external electrostatic potential. The latter describes a relativistic quantum electron moving in the field of some (pointwise or extended) nuclei. The main question we ask is whether the eigenvalue is minimal when the nuclear charge is concentrated at one single point. This well-known property in nonrelativistic quantum mechanics has escaped all attempts of proof in the relativistic case.
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Dates et versions

hal-03619203 , version 1 (25-03-2022)
hal-03619203 , version 2 (12-10-2022)

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Maria Esteban, Mathieu Lewin, Éric Séré. Which Nuclear Shape Generates the Strongest Attraction on a Relativistic Electron? An Open Problem in Relativistic Quantum Mechanics. Mathematics Going Forward, 2313, Springer International Publishing, pp.487-497, 2023, Lecture Notes in Mathematics, ⟨10.1007/978-3-031-12244-6_34⟩. ⟨hal-03619203v2⟩
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