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.