  We investigate the energy spectrum structure of a system of two (identical)
interacting bosonic wells occupied by N bosons within the Schwinger realization
of the angular momentum. This picture enables us to recognize the symmetry
properties of the system Hamiltonian H and to use them for characterizing the
energy eigenstates. Also, it allows for the derivation of the single-boson
picture which is shown to be the background picture naturally involved by the
secular equation for H. After deriving the corresponding eigenvalue equation,
we recast it in a recursive N-dependent form which suggests a way to generate
the level doublets (characterizing the H spectrum) via suitable inner
parameters. Finally, we show how the presence of doublets in the spectrum
allows to recover, in the classical limit, the symmetry breaking effect that
characterizes the system classically.
