Classical probability density function for one particle is defined as an inverse speed or equivalently by the Dirac Delta function. We compare quantum and classical probability density of position and momentum with regarding Correspondence principle. Examples include bound and also unbound potentials. In addition, some spherically symmetric potentials are solved and the first order classical perturbation corresponding to the first order quantum perturbation is drived. Perturbed energy calculated for Kepler–Coulomb and harmonic oscillator potentials agree with change of energy in the precession of the ellipse or in the spin-orbit magnetic interaction. Afterwards , we introduce quantum and classical joint probability density of position and momentum. With this approach correspondence between description of classical and quantum free particles is concluded , although possible troubles with respect to distinguishability of classical particles is expressed in there . In the next section, we propose a mass density model of mutually exclusive particles instead of continues mass density with the help of squre wave function and classical probability density. We indicate that, how averaging by this model for infinity particles correspond to that of continues mass density. Then we return to one particle problem for calculating and comparing classical and quantum uncertainty. Analytic results are former; including infinite well, bouncing ball and harmonic oscillator potentials. Later, we numerically compare classical and quantum uncertainty for symmetric and asymmetric potentials. In this comparison, analytically driven equivalents vanish with changing potential intervals. Besides this conclusion , some programing explanations are mentioned too.
