In this talk work where the two-site Bose–Hubbard model was studied analytically in the limit of weak coupling u and large number of particles N will be reported. In particular, the difference in the occupation between the two sites, where initially all particles are at one site, was calculated analytically. This quantity exhibits collapses and revivals that superimpose rapid oscillations. Excellent agreement with the exact numerical solution was found. The semiclassical approximation where 1/N plays the role of Planckʼs constant was used and for large N it is superior to standard quantum perturbation theory. The occupation difference was calculated also for the case where initially both sites are occupied provided that the difference in occupation is sufficiently large. This work 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.Examples will be presented. Joint Work with Hagar Veksler.