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Supersymmetric quantum mechanics with reflections

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 05 Oct 2011Embargo end date: 01 Jan 2011Publisher:IOP PublishingJournal:Journal of Physics A: Mathematical and Theoretical, volume 44, page 435,301 (issn: 1751-8113, eissn: 1751-8121,

Authors: Luc Vinet; Alexei Zhedanov; Sarah Post;

doi: 10.1088/1751-8113/44/43/435301 , 10.48550/arxiv.1107.5844

arXiv: http://arxiv.org/abs/1107.5844

Supersymmetric quantum mechanics with reflections

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Abstract

We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q-> -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wave functions of extended Scarf I potentials with different parameters are presented.

17 pages

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Keywords

FOS: Physical sciences, Mathematical Physics (math-ph), 15A18, 05E35, 33D45, 34Kxx, 81Q60, Mathematical Physics

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