  A mathematically rigorous derivation of the first Vlasov equation as a
well-known Schr\"odinger equation for the probabilistic description of a system
and families of the classic diffusion equations and heat conduction for the
deterministic description of physical systems was inferred. A physical meaning
of the phase of the wave function which is a scalar potential of the
probabilistic flow velocity is demonstrated. Occurrence of the velocity
potential vortex component leads to the Pauli equation for one of the spinar
components. A scheme of the construction of the Schr\"odinger equation solving
from the Vlasov equation solving and vice-versa is shown. A process of
introduction of the potential to the Schr\"odinger equation and its
interpretation are given. The analysis of the potential properties gives us the
Maxwell equation, the equation of the kinematic point movement, and the
movement of the medium within electromagnetic fields equation.
