  The dynamics of a Bose-Einstein condensate in a double-well potential are
analysed in terms of transitions between energy eigenstates. By solving the
time-dependent and time-independent Gross-Pitaevskii equation in one dimension,
we identify tunnelling resonances associated with level crossings, and
determine the critical velocity that characterises the resonance. We test the
validity of a non-linear two-state model, and show that for the experimentally
interesting case, where the critical velocity is large, the influence of
higher-lying states is important.
