Darboux transformations for time-dependent Schrodinger equations with effective mass

The formalism of Darboux transformations is established for time-dependent Schrodinger equations with an effective (position-dependent) mass. Explicit formulas axe obtained for the transformed wave function and the difference between the original and the transformed potential. It is shown that for a noneffective mass our Darboux transformation reduces correctly to the well-known Darboux transformation.