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We analyze molecular bound states of atomic quantum gases near a Feshbachresonance. A simple, renormalizable field theoretic model is shown to haveexact solutions in the two-body sector, whose binding energy agrees well withobserved experimental results in both Bosonic and Fermionic cases. Thesesolutions, which interpolate between BEC and BCS theories, also provide a moregeneral variational ansatz for resonant superfluidity and related problems.Comment: Minor changes -- to match the final published versio

Coherent molecular bound states of bosons and fermions near a Feshbach resonance