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The dynamical equation of quantum mechanics are rewritten in form ofdynamical equations for the measurable, positive marginal distribution of theshifted, rotated and squeezed quadrature introduced in the so called"symplectic tomography". Then the possibility of a purely classical descriptionof a quantum system as well as a reinterpretation of the quantum measurementtheory is discussed and a comparision with the well known quasi-probabilitiesapproach is given. Furthermore, an analysis of the properties of this marginaldistribution, which contains all the quantum information, is performed in theframework of classical probability theory. Finally examples of harmonicoscillator's states dynamics are treated.Comment: 29 pages,LATEX,accepted by Foundations of Physic

Classical-like description of quantum dynamics by means of symplectic tomography