  We revisit the coherent or delocalized to self-trapping transition in an
interacting bosonic quantum fluid confined in a double well potential, in the
context of full quantum calculations. We show that an $N$-particle Bose-Hubbard
fluid reaches an stationary state through the two-body interactions. These
stationary states are either delocalized or self-trapped in one of the wells,
the former appearing as coherent oscillations in the mean-field approximation.
By studying one- and two-body properties in the energy eigenstates and in a set
of coherent states, we show that the delocalized to self-trapped transition
occurs as a function of the energy of the fluid, provided the interparticle
interaction is above a critical or threshold value. We argue that this is a
type of symmetry-breaking continuous phase transition.
