>The Schrodinger equation is linear

Is it though? Or have we just found a linear approximation to actual reality?

Also, the other day, I read in another HN thread that there are situations (Bose Einstein condensates) where the potential may depend on Psi thus making the equation non-linear (since the potential multiplies Psi).

Besides being a joke, I was a dispersive PDE guy and so have a perverted idea of what the Schroedinger equation is. It’s common in that field to study a nonlinear variant. A u|u|^2 term, for instance, admits sech type solutions.