1999/04/26 by H. C. Rosu
Physics and Astronomy · #quant-ph
published as Int. J. Theor. Phys. 39 (Sept. 2000) 2191-2196 · 6 pages, LaTex, a phrase more with respect to v1 (Don't work on sign errors during weekends!)
arxiv created 1999/04/26 · arxiv updated 2009/12/01
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 ± x 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