  We construct many particle Hamiltonians for which the Laughlin and Jain
wavefunctions are exact ground states. The Hamiltonians involve fermions in a
magnetic field and with inter-particle interactions. For the Laughlin
wave-functions,the interactions involve two- and three-body correlations
similar to the Chern-Simons interactions, whereas for the projected Jain
wave-functions, N-body interactions (which cannot be explicitly written down in
general) are involved.
