Supersymmetric quantum mechanics and the inverse scattering method

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Abstract
The procedures for finding a new potential (1) by eliminating the ground state of a given potential, (2) by adding a bound state below the ground state of a given potential and (3) by generating the phase equivalent family of a given potential using the supersymmetric pairing of the spectra of the operators A+A- and A-A+ are compared with the application of the Gelfand-Levitan procedure (1955) for the corresponding cases. It is shown how the equivalence of the two procedures may be established. A distinction is made between the modifications of the Jost functions associated with four different types of transformations generated by the concept of a supersymmetric partner to a given Schrodinger equation. It is shown that the Bargmann class of potentials may be generated using suitable combinations of the four types of transformations.