  The dynamical equation of quantum mechanics are rewritten in form of
dynamical equations for the measurable, positive marginal distribution of the
shifted, rotated and squeezed quadrature introduced in the so called
"symplectic tomography". Then the possibility of a purely classical description
of a quantum system as well as a reinterpretation of the quantum measurement
theory is discussed and a comparision with the well known quasi-probabilities
approach is given. Furthermore, an analysis of the properties of this marginal
distribution, which contains all the quantum information, is performed in the
framework of classical probability theory. Finally examples of harmonic
oscillator's states dynamics are treated.
