  We consider the stationary solutions for a class of Schroedinger equations
with a symmetric double-well potential and a nonlinear perturbation. Here, in
the semiclassical limit we prove that the reduction to a finite-mode
approximation give the stationary solutions, up to an exponentially small term,
and that symmetry-breaking bifurcation occurs at a given value for the strength
of the nonlinear term. The kind of bifurcation picture only depends on the
non-linearity power. We then discuss the stability/instability properties of
each branch of the stationary solutions. Finally, we consider an explicit
one-dimensional toy model where the double well potential is given by means of
a couple of attractive Dirac's delta pointwise interactions.
