Derivation of the Schrödinger–Poisson equation from the quantum 𝐍-body problem
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.

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DOI: 10.1016/S1631-073X(02)02253-7
Bardos, Claude 1; Erdös, Laszlo 2; Golse, François 1; Mauser, Norbert 3; Yau, Horng-Tzer 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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     title = {Derivation of the {Schr\"odinger{\textendash}Poisson} equation from the quantum $ \mathbf{N}$-body problem},
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Bardos, Claude; Erdös, Laszlo; Golse, François; Mauser, Norbert; Yau, Horng-Tzer. 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. http://www.numdam.org/articles/10.1016/S1631-073X(02)02253-7/

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