q deformation by intertwining with application to the singular oscillator
arXiv:quant-ph/9808021 · doi:10.1016/S0375-9601(99)00846-4
Abstract
We present a version of q-deformed calculus based on deformed counterparts of Darboux intertwining operators. The case in which the deformed transformation function is of the vacuum type is detailed, but the extension to counterparts of excited states used as Darboux transformation functions is also formally discussed. The method leads to second-order Fokker-Planck-like deformed operators which may be considered as supersymmetric partners, though for a sort of q-deformed open systems, i.e., those possessing q nonlocal drift terms, potential part, as well as q-spreaded vacuum fluctuations. The undeformed limit corresponds to the conservative case, since all q nonlocalities wash out. The procedure is applied to the x^{-2} singular oscillator, for which we also present a formal q generalization of the Bagrov-Samsonov coherent states
10 pages, accepted at Phys. Lett. A
References in corpus (5)
- Quantum singular oscillator as a model of two-ion trap: an amplification of transition probabilities due to small time variations of the binding potential
- Non-linear coherent states associated with conditionally exactly solvable problems
- Ladder operators for isospectral oscillators
- Solvable potentials, non-linear algebras, and associated coherent states
- Distortion of a Phase Space Under the Darboux Transformation