Husimi Parametric Oscillator in Frame of Symplectic Group and Q-oscillators

Abstract

Time--dependent integrals of motion which are linear forms in position and momentum are discussed for Husimi parametric forced oscillator. Generalization of these integrals of motion for q--oscillator is presented. Squeezing and quadrature correlation phenomena are discussed on the base of Schr\"odinger uncertainty relation. The properties of the generalized correlated states, squeezed states, even and odd coherent states (the Schr\"odinger cat states) are reviewed. The relation of the constructed nonclassical states to representations of the symplectic symmetry group and finite symmetry groups is discussed.