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Between Schroedinger and Hermite: Supersymmetric pair of q-deformed non-local operators

H. C. Rosu
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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 $\pm x$ 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

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H. C. Rosu. 1999-04-26. Between Schroedinger and Hermite: Supersymmetric pair of q-deformed non-local operators. https://arxiv.org/abs/quant-ph/9904046

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