  We study the Bose-Einstein condensate in the MIT double-well trap. We
calculate the ground state density profile of $^{23}$Na atoms and the
Bogoliubov spectrum of the elementary excitations as function of the strength
of the double-well barrier. In particular, we analyze the behavior of
quantum-mechanical collective excitations. Finally, we discuss the
observability criteria for macroscopic quantum tunneling and macroscopic
quantum self-trapping.
