  We present a solution of the three-fermion problem in a harmonic potential
across a Feshbach resonance. We compare the spectrum with that of the two-body
problem and show that it is energetically unfavorable for the three fermions to
occupy one lattice site rather than two. We also demonstrate the existence of
an energy level crossing in the ground state with a symmetry change of its wave
function, suggesting the possibility of a phase transition for the
corresponding many-body case.
