q-deformation by intertwinning with application to the singular oscillator

We present a Version of q-deformed calculus based on deformed counterparts of Darboux intertwining operators. The case in which the deformed transform ation function is of the vacuum type is detailed, but the extension to coun terparts of excited states used as Darboux transformation functions is also formally discussed. The method lends to second-order Fokker-Planck-like de formed operators which may be considered as supersymmetric partners, though for a sort of q-deformed open systems, i.e., those possessing q nonlocal d rift terms, potential part, as well as q-spreaded vacuum fluctuations. The undeformed limit corresponds to the conservative case, since all q nonlocal ities wash out. The procedure x(-2) singular oscillator, for which we also present a formal rl generalization of the Bagrov-Samsonov applied to the x( -2) coherent states. (C) 2000 Published by Elsevier Science B.V. All rights reserved.