We have developed a field-theory approach for solving the dynamics of a Bose gas at zero temperature in a double-well potential beyond the Gross-Pitaevskii equation where all the particles reside in a single spatial mode.  This method supplies predictions of coherence, number-phase uncertainty and deterministic or random interference in a double-well potential varying in time. It also generalizes the conventional Bose-Hubbard approach for a multiple-well system by supplying predictions of the full spatial evolution in a double-well system with weak or strong tunneling between the wells. We describe the ground-state of such a system and show some examples of the dynamics in interference experiments and Josephson oscillations experiments. We demonstrate how parameters that do not appear in the probability density, such as the number of atoms and the phase uncertainty between different parts of the system, are important for subsequent evolution of the matter-waves.