Laszlo Erdos, Horng-Tzer Yau
Derivation of the nonlinear Schr\"odinger equation with a Coulomb potential
(80K, LaTeX)
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.