  We study the short-time dynamics of a degenerate Fermi gas positioned near a
Feshbach resonance following an abrupt jump in the atomic interaction resulting
from a change of external magnetic field. We investigate the dynamics of the
condensate order parameter and pair wavefunction for a range of field
strengths. When the abrupt jump is sufficient to span the BCS to BEC crossover,
we show that the rigidity of the momentum distribution precludes any
atom-molecule oscillations in the entrance channel dominated resonances
observed in the 40K and 6Li. Focusing on material parameters tailored to the
40K Feshbach resonance system at 202.1 gauss, we comment on the integrity of
the fast sweet projection technique as a vehicle to explore the condensed phase
in the crossover region
