On the coherent states, displacement operators and quasidistributions associated with deformed quantum oscillators

The Wigner (W), Husimi-Kano (Q) and Glauber-Sudarshan (P) quasidistributions are generalized to f-deformed quasidistributions which extend the parametric family of s-ordered quasidistributions of Cahill and Glauber. The deformation procedure is obtained via a canonical nonisometric transform of the displacement operators which preserves the form of the standard creation-annihilation commutation relation, hence the Heisenberg-Weyl algebra, but changes the scalar product in the Hilbert space of the oscillator states. A whole class of new resolutions of the identity is introduced. The time evolution equation for the new generalized quasidistributions is derived.