Supersymmetric Quantum Mechanics with Reflections

Details Supersymmetric Quantum Mechanics with Reflections Supersymmetric Quantum Mechanics with Reflections

2011-07-28

arxiv.org/abs/1107.5844v2

J.Phys.A44:435301,2011

Physics

Mathematical Physics

17 pages

Scientific paper

10.1088/1751-8113/44/43/435301

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.

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