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We present a representative set of analytic stationary state solutions of theNonlinear Schr\"odinger equation for a symmetric double square well potentialfor both attractive and repulsive nonlinearity. In addition to the usualsymmetry preserving even and odd states, nonlinearity introduces quite exoticsymmetry breaking solutions - among them are trains of solitons with differentnumber and sizes of density lumps in the two wells. We use the symmetrybreaking localized solutions to form macroscopic quantum superpositions statesand explore a simple model for the exponentially small tunneling splitting.Comment: 11 pages, 11 figures, revised version, typos and references correcte

Bose-Einstein condensates in a one-dimensional double square well: Analytical solutions of the nonlinear Schrödinger equation