Wave function in classical statistical mechanics

The possibility to formulate classical statistical mechanics in terms of the complex wave function and density matrix obeying the evolution equation is discussed. It is shown that the modulus squared of the introduced wave function of the classical particle has the same physical meaning as the modulus squared of the wave function of the quantum particle. The tomographic probabilities are studied for both classical and quantum states. Integrals of motion and their relation to the propagators are discussed.