  In this work the two site Bose-Hubbard model is studied analytically in the
limit of weak coupling u and large number of particles N . The semiclassical
approximation where \frac{1}{N} plays the role of Planck's constant was used
and perturbation theory to order u^{2} was applied. In particular, the
difference in the occupation between the two sites, where initially all
particles are at one site was calculated analytically. Excellent agreement with
the exact numerical solution was found. This quantity exhibits collapses and
revivals that superimpose rapid oscillations. The occupation difference was
calculated also for the case where initially both sites are occupied provided
that the difference in occupation is sufficiently large. It provides an
analytical description of results that were so far found only numerically.
Similar behavior and analysis are expected for a large variety of physical
situations in optics, atom optics and quantum dynamics of electrons in Rydberg
atoms.
