Supersymmetric Quantum Mechanics with Reflections
Mathematical Physics
2011-10-11 v2 math.MP
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.
Cite
@article{arxiv.1107.5844,
title = {Supersymmetric Quantum Mechanics with Reflections},
author = {S. Post and L. Vinet and A. Zhedanov},
journal= {arXiv preprint arXiv:1107.5844},
year = {2011}
}
Comments
17 pages