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Derivation of the Schrödinger-Poisson equation from the quantum \(N\)-body problem. (English. Abridged French version) Zbl 1018.81009

Summary: We derive the time-dependent Schrödinger-Poisson equation as the weak coupling limit of the \(N\)-body linear Schrödinger equation with Coulomb potential.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
35J10 Schrödinger operator, Schrödinger equation
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