Nonstationary quantum systems and entanglement in the tomographic-probability representation

Time-dependent integrals of motion for systems with both time-independent and time-dependent Hamiltonians are studied and expressed in terms of the evolution operator. The probability representation in which the system quantum states are described by tomographic probabilities (tomograms), is reviewed. Examples of systems of parametric oscillators and the entanglement phenomena induced by time-dependent coupling of the oscillators are discussed. Transition probabilities between the energy levels of parametric oscillators expressed in terms of special functions like Laguerre and Legendre polynomials are given in terms of tomographic probabilities