P. Aniello et al., On the coherent states, displacement operators and quasidistributions associated with deformed quantum oscillators, J OPT B-QUA, 2(6), 2000, pp. 718-725
The Wigner (W), Husimi-Kano (Q) and Glauber-Sudarshan (P) quasidistribution
s are generalized to f-deformed quasidistributions which extend the paramet
ric family of s-ordered quasidistributions of Cahill and Glauber. The defor
mation procedure is obtained via a canonical nonisometric transform of the
displacement operators which preserves the form of the standard creation-an
nihilation commutation relation, hence the Heisenberg-Weyl algebra, but cha
nges the scalar product in the Hilbert space of the oscillator states. A wh
ole class of new resolutions of the identity is introduced. The time evolut
ion equation for the new generalized quasidistributions is derived.