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Phase equivalent potentials, Complex coordinates and Supersymmetric Quantum Mechanics

C. V. Sukumar
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Abstract

Supersymmetric Quantum Mechanics may be used to construct reflectionless potentials and phase-equivalent potentials. The exactly solvable case of the $λsech^2$ potential is used to show that for certain values of the strength $λ$ the phase-equivalent singular potential arising from the elimination of all the boundstates is identical to the original potential evaluated at a point shifted in the complex cordinate space. This equivalence has the consequence that certain general relations valid for reflectionless potentials and phase-equivalent potentials lead to hitherto unknown identities satisfied by the Associated Legendre functions. This exactly solvable probelm is used to demonstrate some aspects of scattering theory.

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C. V. Sukumar. 2006-11-01. Phase equivalent potentials, Complex coordinates and Supersymmetric Quantum Mechanics. https://doi.org/10.1088/0305-4470/39/46/017

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