We construct explicit Darboux transformations of arbitrary order for a class of generalized, linear Schrödinger equations. Our construction contains the well-known Darboux transformations for Schrödinger equations with position-dependent mass, Schrödinger equations coupled to a vector potential and Schrödinger equations for weighted energy.
We establish the supersymmetry formalism for time-dependent Schrödinger equations with effective mass and show that the corresponding supersymmetric transformations are equivalent to effective mass Darboux transformations
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