  The spectrum of two spin-up and two spin-down fermions in a trap is
calculated using a correlated gaussian basis throughout the range of the
BCS-BEC crossover. These accurate calculations provide a few-body solution to
the crossover problem. This solution is used to study the time-evolution of the
system as the scattering length is changed, mimicking experiments with Fermi
gases near Fano-Feshbach resonances. The structure of avoiding crossings in the
spectrum allow us to understand the dynamics of the system as a sequence of
Landau-Zener transitions. Finally, we propose a ramping scheme to study
atom-molecule coherence.

Superconductivity;Nuclear Theory;Atomic Physics;Quantum Physics