We consider the process of diffusion scattering of a wave function given on thephase space. In this process the heat diffusion is considered only along momenta. We writedown the modified Kramers equation describing this situation. In this model, the usual quantumdescription arises as asymptotics of this process for large values of resistance of the medium perunit of mass of particle. It is shown that in this case the process passes several stages. During thefirst short stage, the wave function goes to one of “stationary” values. At the second long stage,the wave function varies in the subspace of “stationary” states according to the Schrodingerequation. Further, dissipation of the process leads to decoherence, and any superposition ofstates goes to one of eigenstates of the Hamilton operator. At the last stage, the mixed stateof heat equilibrium (the Gibbs state) arises due to the heat influence of the medium and therandom transitions among the eigenstates of the Hamilton operator. Besides that, it is shownthat, on the contrary, if the resistance of the medium per unit of mass of particle is small, thenin the considered model, the density of distribution of probability ρ = |?|2 satisfies the standardLiouville equation, as in classical statistical mechanics.
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