  We present the theory of a pair of atoms in a one-dimensional optical lattice
interacting via a narrow Feshbach resonance. Using a two-channel description of
the resonance, we derive analytic results for the scattering states inside the
continuum band and the discrete bound states outside the band. We identify a
Fano resonance profile, and the survival probability of a molecule when swept
through the Bloch band of scattering states by varying an applied magnetic
field. We discuss how these results may be used to investigate the importance
of the structured nature of the continuum in experiments.
