The finite difference algorithm for higher order supersymmetry

Abstract

The higher order supersymmetric partners of the Schroedinger's Hamiltonians can be explicitly constructed by iterating a simple finite difference equation corresponding to the Baecklund transformation. The method can completely replace the Crum determinants. Its limiting, differential case offers some new operational advantages.

LaTeX, 12 pages, 3 figures. To appear in Phys. Lett. A

References in corpus (4)

• A family of complex potentials with real spectrum
• New hydrogen-like potentials
• Exactly Solvable Hydrogen-like Potentials and Factorization Method
• New Families of Isospectral Hydrogen-like potentials

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