SUPERSYMMETRIC QUANTUM-MECHANICS AND THE INVERSE SCATTERING METHOD

Journal article

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.

Authors: Sukumar, C

• Publication status: Published
• Journal: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
• Volume: 18
• Issue: 15
• Pages: 2937-2955
• Publication date: 1985-01-01
• DOI: 10.1088/0305-4470/18/15/021
• EISSN: 1361-6447
• ISSN: 0305-4470
• Language: English