Comptes Rendus
no. 6
Derivation of the Schrödinger–Poisson equation from the quantum 𝐍-body problem
[Justification de l'équation de Schrödinger–Poisson à partir du problème quantique à N corps]
Claude Bardos1 ; Laszlo Erdös2 ; François Golse1 ; Norbert Mauser3 ; Horng-Tzer Yau4
1 Université Paris 6, Laboratoire d'analyse numérique, 175, rue du Chevaleret, 75013 Paris, France
2 School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA
3 Wolfgang Pauli Institute, c/o Inst. f. das Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
4 Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA
Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 515-520.

We derive the time-dependent Schrödinger–Poisson equation as the weak coupling limit of the N-body linear Schrödinger equation with Coulomb potential.

On établit la validité de l'équation de Schrödinger–Poisson en régime instationnaire comme limite à couplage faible de l'équation de Schrödinger linéaire à N corps avec potentiel de Coulomb.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02253-7

Claude Bardos 1 ; Laszlo Erdös 2 ; François Golse 1 ; Norbert Mauser 3 ; Horng-Tzer Yau 4

1 Université Paris 6, Laboratoire d'analyse numérique, 175, rue du Chevaleret, 75013 Paris, France
2 School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA
3 Wolfgang Pauli Institute, c/o Inst. f. das Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
4 Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA 
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Claude Bardos; Laszlo Erdös; François Golse; Norbert Mauser; Horng-Tzer Yau. Derivation of the Schrödinger–Poisson equation from the quantum $ \mathbf{N}$-body problem. Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 515-520. doi : 10.1016/S1631-073X(02)02253-7. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02253-7/

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