  We propose to experimentally realize an odd parity eigenstate $\left\vert
b\right\rangle $ of two atoms in the double well. The occupation probability of
this state shows evident dependence on the interaction, distinct from the
result of two-mode model adopted in the Heidelberg experiment. The tunneling
dynamics of two atoms starting from the $NOON$ state with infinite barrier
height can be derived from the exactly solved model of $\delta $-barrier split
double well based on a Bethe ansatz type hypothesis of the wave functions. We
find that the single particle tunneling transfer the probabilities between
double occupancy and single occupancy of each well.
