Explicit Darboux transformations of arbitrary order for generalized time-dependent Schroedinger equations

We construct Darboux transformations of arbitrary order for a generalized, linear, time-dependent Schroedinger equation, special cases of which correspond to time-dependent Hamiltonians coupled to a magnetic field, with position-dependent mass and with weighted energy. Our Darboux transformation reduces correctly to these known cases and also to new, generalized Schroedinger equations. Furthermore, fundamental properties of the conventional Darboux transformation are maintained, such as factorization of the nth order transformation into first-order transformations and existence of a reality condition for the transformed potentials