Darboux transformation for the nonstationary Schroedinger equation

The Darboux transformation is introduced for the one-dimensional nonstationary Schroedinger equation. The operator of this transformation is a differential operator of the N order and it transforms the solutions of an equation with a given potential into the solutions with a new potential, which is constructed from the solutions of the initial equation. A connection is established of the given transformation with the supersymmetric quantum mechanics. Operators for the conserved in time supercharge are introduced. The stationary states of the operators turn into known ones. Examples are given of exactly solved nonstationary potentials of elementary kind. 12 refs