When a 2D many-particle system with a repulsive interaction is subject to a suff iciently strong magnetic field, that can also be produced by rapid rotation, str ongly correlated many-body states in the lowest Landau level LLL may emerge. In the talk conditions for the ground state to include the Laughlin state as a fact or will be presented, together with an analysis of the particle density in such states. This is joint work with Sylvia Serfaty and Nicolas Rougerie.