  Based on the concept of ensemble, it is proved in the manuscript that the
probability amplitude function can also been used to describe the classical
statistical system. The motion equations of probability amplitude functions of
classical statistical system are obtained, which are similar to that in quantum
mechanics. It is also proved in the meantime that microsystems that obey
quantum mechanics can also be described in the forms of classical statistical
mechanics and deterministic classical mechanics. The quantum revised formula of
classical interaction force and the revised Liouville's equations are also
obtained. In this way, the transformation of two descriptive forms between
classical mechanics and quantum mechanics is achieved. A new and rational
interpretation about quantum mechanics, including the meaning of wave function,
the potential barrier penetration of microparticles, the Uncertainty relation,
the wave-particle duality, the essence of spin and the Bell's inequality and so
on, is provided in the paper. Based on the transformation, two fundamental
hypotheses are put forward as the basic postulates of classical statistical
physics. The equal probability hypothesis in the equilibrium states is given
up. The united description of nonequilibrium state mechanics and equilibrium
state statistical mechanics is reached, and the so-called reversibility paradox
can also be eliminated.
