TY - JOUR AB - We study the ground state of a trapped Bose gas, starting from the full many-body Schrödinger Hamiltonian, and derive the non-linear Schrödinger energy functional in the limit of a large particle number, when the interaction potential converges slowly to a Dirac delta function. Our method is based on quantitative estimates on the discrepancy between the full many-body energy and its mean-field approximation using Hartree states. These are proved using finite dimensional localization and a quantitative version of the quantum de Finetti theorem. Our approach covers the case of attractive interactions in the regime of stability. In particular, our main new result is a derivation of the 2D attractive non-linear Schrödinger ground state. AU - Lewin, Mathieu AU - Nam, Phan AU - Rougerie, Nicolas ID - 1491 IS - 9 JF - Transactions of the American Mathematical Society TI - The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases VL - 368 ER -