Squeezed and Correlated States of Parametric Oscillator and Free Particle in the Probability Representation of Quantum Mechanics

The states of quantum oscillator with time-dependent frequency are described by the tomographic probability distributions. The integrals of motion, being linear in the position and momentum operators, are used to construct the Gaussian squeezed and correlated states of the oscillator associated with normal probability distributions of the quadrature determining the density matrices of the states. The even and odd coherent states of the oscillator and their symplectic tomograms are given in terms of probability distributions. Considering free particle as a partial case of the oscillator with zero frequency, we find tomograms of even and odd coherent states of free particle in the probability representation.