  A semiclassical Bohr-Sommerfeld approximation is derived for an N-particle,
two-mode Bose-Hubbard system modeling a Bose-Einstein condensate in a
double-well potential. This semiclassical description is based on the
`classical' dynamics of the mean-field Gross-Pitaevskii equation and is
expected to be valid for large N. We demonstrate the possibility to reconstruct
quantum properties of the N-particle system from the mean-field dynamics. The
resulting semiclassical eigenvalues and eigenstates are found to be in very
good agreement with the exact ones, even for small values of N, both for
subcritical and supercritical particle interaction strength where tunneling has
to be taken into account.
