Properties of some nonlinear Schrodinger equations motivated through information theory

Abstract: We update our understanding of nonlinear Schrodinger equations motivated through information theory. In particular we show that a $q-$deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system, thus favouring the simplest $q=1$ case. Furthermore the energy minimisation criterion is shown to be equivalent, at leading order, to an uncertainty maximisation argument. The special value $η=1/4$ for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, $η$ might be encoding relativistic effects.