2007, Vol.14, pp.228-241

By using the intertwining operator technique we show how to construct the quantum well potential with a desired spectrum for the Schrödinger equation with a position-dependent effective mass. The first- and second-order Darboux transformations, supersymmetry, chain of transformations are considered for the Schrödinger equation with a nonconstant mass. An interrelation is established between the differential and integral transformation operators. The method allows one to generate potentials with additional and with removal bound states in comparison with the spectrum of an initial potential as well as to construct phase-equivalent potentials.
Key words: quantum well, inverse scattering problem, intertwining operator technique, Darboux transformation

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