Erdos, LaszloSchlein, BenjaminYau, Horng-Tzer2017-05-182006Erdos, László, Benjamin Schlein, and Horng-Tzer Yau. 2006. “Derivation of the Cubic Non-Linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems.” Inventiones Mathematicae 167 (3) (December 20): 515–614. doi:10.1007/s00222-006-0022-1.0020-9910http://nrs.harvard.edu/urn-3:HUL.InstRepos:32706730We 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 Schrödinger equation in a suitable scaling limit. The result is extended to k-particle density matrices for all positive integer k.en-USFeynman diagramsBBGKY hierarchydispersive estimatespropagation of chaosJournal Article2017-05-1810.1007/s00222-006-0022-1