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

摘要

We construct Darboux transformations of arbitrary order for a generalized, linear, time-dependent Schr_dinger 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 Schr_dinger 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.