  We analyze molecular bound states of atomic quantum gases near a Feshbach
resonance. A simple, renormalizable field theoretic model is shown to have
exact solutions in the two-body sector, whose binding energy agrees well with
observed experimental results in both Bosonic and Fermionic cases. These
solutions, which interpolate between BEC and BCS theories, also provide a more
general variational ansatz for resonant superfluidity and related problems.
