Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate

Abstract

Consider a system of N bosons in three dimensions interacting via a repulsive short range pair potential N 2 V .N.x i x j //, where x D .x 1 ; : : : ; x N / denotes the positions of the particles. Let H N denote the Hamiltonian of the system and let N;t be the solution to the Schrdinger equation. Suppose that the initial data N;0 satisfies the energy condition