  We introduce higher dimensions into the problem of Bose-Einstein condensates
in a double-well potential, taking into account orbital angular momentum. We
completely characterize the eigenstates of this system, delineating new regimes
via both analytical high-order perturbation theory and numerical exact
diagonalization. Among these regimes are mixed Josephson- and Fock-like
behavior, crossings in both excited and ground states, and shadows of
macroscopic superposition states.
