  We compare the classical (mean-field) dynamics with the quantum dynamics of
atomic Bose-Einstein condensates in double-well potentials. The quantum
dynamics are computed using a simple scheme based upon the Raman-Nath
equations. Two different methods for exciting a non-equilbrium state are
considered: an asymmetry between the wells which is suddenly removed, and a
periodic time oscillating asymmetry. The first method generates wave packets
that lead to collapses and revivals of the expectation values of the
macroscopic variables, and we calculate the time scale for these revivals. The
second method permits the excitation of a single energy eigenstate of the
many-particle system, including Schroedinger cat states. We also discuss a band
theory interpretation of the energy level structure of an asymmetric
double-well, thereby identifying analogies to Bloch oscillations and Bragg
resonances. Both the Bloch and Bragg dynamics are purely quantum and are not
contained in the mean-field treatment.
