The problem of molecular production from a degenerate gas of fermions at a broad Feshbach resonance, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction and induced coherence lead to significant renormalization of the gap between adiabatic levels. The essential region of energies near the resonance contributing to the atom-molecule transformation strongly exceeds the Fermi energy of the weakly interacting gas. The close vicinity of the exact resonance does not play as substantial a role as in the static problem. Our main results are: i) The molecular production is sensitive to the initial magnetic field. ii) In the inverse process of molecule dissociation a large BCS condensate distributed over a broad range of momenta is generated.