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&#39;s theorem on hidden variables. It is shown that the original conditions of the von Neumann&#39;s theorem are not satisfied. In particular, the quantum mechanics cannot describe the particle momentum distribution. The distribution $w(\mathbf{p}) =| ψ_{p%}| ^{2}$ is not a particle momentum distribution at the state $ψ$, 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.