  A model describing coherent quantum tunneling between two trapped
Bose-Einstein condensates is shown to admit an exact solution. The spectrum is
obtained by the algebraic Bethe ansatz. An asymptotic analysis of the Bethe
ansatz equations leads us to explicit expressions for the energies of the
ground and first excited states in the limit of {\it weak} tunneling and all
energies for {\it strong} tunneling. The results are used to extract the
asymptotic limits of the quantum fluctuations of the boson number difference
between the two Bose-Einstein condensates and to characterize the degree of
coherence in the system.
