Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems

Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau

Published 2005-08-02, updated 2007-02-27Version 3

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 $k$.