  David Bohm shown that the Schr{\"o}dinger equation, that is a "visiting card"
of quantum mechanics, can be decomposed onto two equations for real functions -
action and probability density. The first equation is the Hamilton-Jacobi (HJ)
equation, a "visiting card" of classical mechanics, to be modified by the
Bohmian quantum potential. And the second is the continuity equation. The
latter can be transformed to the entropy balance equation. The Bohmian quantum
potential is transformed to two Bohmian quantum correctors. The first corrector
modifies kinetic energy term of the HJ equation, and the second one modifies
potential energy term. Unification of the quantum HJ equation and the entropy
balance equation gives complexified HJ equation containing complex kinetic and
potential terms. Imaginary parts of these terms have order of smallness about
the Planck constant. The Bohmian quantum corrector is indispensable term
modifying the Feynman's path integral by expanding coordinates and momenta to
imaginary sector.
