  We relate the quantum dynamics of the Bose-Hubbard model (BHM) to the
semiclassical nonlinear equations that describe an array of interacting Bose
condensates by implementing a standard variational procedure based on the
coherent state method. We investigate the dynamics of the two-site BHM from the
purely quantum viewpoint by recasting first the model within a spin picture and
using then the related dynamical algebra. The latter allows us to study
thoroughly the energy spectrum structure and to interpret quantally the
classical symmetries of the two-site dynamics. The energy spectrum is also
evaluated through various approximations relying on the coherent state
approach.
