- 01-433 Laszlo Erdos, Horng-Tzer Yau
- Derivation of the nonlinear Schr\"odinger equation with a Coulomb potential
Nov 21, 01
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Abstract. We consider the time evolution of $N$ bosonic particles
interacting via a mean field Coulomb potential.
Suppose the initial state is a product wavefunction.
We show that at any finite time the correlation
functions factorize in the limit $N \to \infty$.
Furthermore, the limiting one particle density matrix
satisfies the nonlinear Hartree equation. The
key ingredients are the uniqueness of the BBGKY hierarchy
for the correlation functions and a new apriori
estimate for the many-body Schr\"odinger equations.