Some general aspects regarding classical dynamical systems and quantum systems are presented. In the classic case, the continuity equation for the probability density and the Liouville theorem about the evolution of volumes in the phase space are presented. For the quantum description of the systems in the states space are presented the Schrodinger equation on the basis of which the probability density of locating the systems in the state space is built. In order to bene t from the formalism of quantum physics, the Liouville operator is identi ed in the classical case, whose eigenvectors can determine a base in the phase space similar to the basic states of a Hermitian operator from quantum physics. The existing results in the literature are systematized in an original formulation.