Some open mathematical problems concerning charged quantum particles

Mathieu Lewin

doi:10.5802/crphys.249

Intervention en colloque

Some open mathematical problems concerning charged quantum particles
[Quelques problèmes mathématiques ouverts sur les particules quantiques chargées]

Mathieu Lewin ¹

¹ CEREMADE, CNRS and Université Paris Dauphine - PSL, Place de Lattre de Tassigny, 75 016 PARIS, France

Comptes Rendus. Physique, Volume 26 (2025), pp. 369-380.

Cet article fait partie du numéro thématique Questions ouvertes dans le problème quantique à N corps coordonné par Yvan Castin et al..

Abstract (VO)
Résumé

I present some open mathematical problems concerning electrons in quantum mechanics and charged particles in general. After discussing the Schrödinger Hamiltonian describing atoms and molecules with classical nuclei, I turn to infinite systems and in particular to the homogeneous electron gas.

Je présente quelques problèmes mathématiques ouverts concernant les électrons en mécanique quantique et les particules chargées en général. Après avoir discuté de l’hamiltonien de Schrödinger décrivant les atomes et les molécules avec des noyaux classiques, je considère les systèmes infinis et en particulier le gaz homogène d’électrons.

Reçu le : 2024-11-06
Révisé le : 2025-03-28
Accepté le : 2025-03-31
Publié le : 2025-05-07

DOI : 10.5802/crphys.249

Keywords: Schrödinger equation, Coulomb systems, Homogeneous electron gas
Mots-clés : Équation de Schrödinger, Systèmes coulombiens, Gaz d’électrons homogène

Affiliations des auteurs :

Mathieu Lewin ¹

¹ CEREMADE, CNRS and Université Paris Dauphine - PSL, Place de Lattre de Tassigny, 75 016 PARIS, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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Mathieu Lewin. Some open mathematical problems concerning charged quantum particles. Comptes Rendus. Physique, Volume 26 (2025), pp. 369-380. doi : 10.5802/crphys.249. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.249/

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