Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau
Derivation of the Cubic Non-linear Schr\"odinger Equation from Quantum Dynamics of Many-Body Systems
(1240K, Postscript)

ABSTRACT.  We prove rigorously that the one-particle density matrix of 
three dimensional 
interacting Bose systems with a short-scale repulsive pair 
interaction converges to the solution of the cubic non-linear 
Schr\"odinger equation in a suitable scaling limit. 
The result is extended to 
$k$-particle density matrices for all positive integer $k$.