Between Schroedinger and Hermite: Supersymmetric pair of q-deformed non-local operators
Abstract
A simple version of the q-deformed calculus is used to generate a pair of q-nonlocal, second-order difference operators by means of deformed counterparts of Darboux intertwining operators for zero factorization energy. These deformed non-local operators may be considered as supersymmetric partners and their structure contains contributions originating in both the Hermite operator and the quantum harmonic oscillator operator. There are also extra contributions. The undeformed limit, in which all q-nonlocalities wash out, corresponds to the usual supersymmetric pair of quantum mechanical harmonic oscillator Hamiltonians. The more general case of negative factorization energy is briefly discussed as well
Keywords
Cite
@article{arxiv.quant-ph/9904046,
title = {Between Schroedinger and Hermite: Supersymmetric pair of q-deformed non-local operators},
author = {H. C. Rosu},
journal= {arXiv preprint arXiv:quant-ph/9904046},
year = {2007}
}
Comments
6 pages, LaTex, a phrase more with respect to v1 (Don't work on sign errors during weekends!)