Hydrodynamical interpretation of quantum mechanics: the momentum distribution

Abstract

The quantum mechanics is considered to be a partial case of the stochastic system dynamics. It is shown that the wave function describes the state of statistically averaged system $<\mathcal{S}_{st}>$, but not that of the individual stochastic system $\mathcal{S}_{st}$. It is a common practice to think that such a construction of quantum mechanics contains hidden variables, and it is incompatible with the von Neumann's theorem on hidden variables. It is shown that the original conditions of the von Neumann's theorem are not satisfied. In particular, the quantum mechanics cannot describe the particle momentum distribution. The distribution $w(\mathbf{p}) =| \psi_{p%}| ^{2}$ is not a particle momentum distribution at the state $\psi $, because it cannot be attributed to a wave function. It is closer to the mean momentum distribution, although the two distributions do not coincide exactly.