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.