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

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 Schrödinger equation in a suitable scaling limit. The result is extended to $k$-particle density matrices for all positive integer $k$.

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