  In a previous paper a formalism to analyze the dynamical evolution of
classical and quantum probability distributions in terms of their moments was
presented. Here the application of this formalism to the system of a particle
moving on a potential is considered in order to derive physical implications
about the classical limit of a quantum system. The complete set of harmonic
potentials is considered, which includes the particle under a uniform force, as
well as the harmonic and the inverse harmonic oscillators. In addition, as an
example of anharmonic system, the pure quartic oscillator is analyzed.
Classical and quantum moments corresponding to stationary states of these
systems are analytically obtained without solving any differential equation.
Finally, dynamical states are also considered in order to study the differences
between their classical and quantum evolution.
