  Quantum dynamics of the Bose-Hubbard Model is investigated through a
semiclassical hamiltonian picture provided by the Time-Dependent Variational
Principle method. The system is studied within a factorized slow/fast dynamics.
The semiclassical requantization procedure allows one to account for the strong
quantum nature of the system when $t/U\ll 1$. The phase diagram is in good
agreement with Quantum Monte Carlo results and third order strong coupling
perturbative expansion.
