  We present a representative set of analytic stationary state solutions of the
Nonlinear Schr\"odinger equation for a symmetric double square well potential
for both attractive and repulsive nonlinearity. In addition to the usual
symmetry preserving even and odd states, nonlinearity introduces quite exotic
symmetry breaking solutions - among them are trains of solitons with different
number and sizes of density lumps in the two wells. We use the symmetry
breaking localized solutions to form macroscopic quantum superpositions states
and explore a simple model for the exponentially small tunneling splitting.
