## On the uncertainty relations in stochastic mechanics.(English)Zbl 1193.81039

Summary: It is shown that the Bohm equations for the phase $$S$$ and squared modulus $$\rho$$ of the quantum mechanical wave function can be derived from the classical ensemble equations admitting an additional momentum $$p_s$$ of the form proportional to the osmotic velocity in the Nelson stochastic mechanics and using the variational principle with appropriate change of variables. The possibility to treat $$\operatorname{grad}S$$ and $$p_s$$ as two parts of the momentum of quantum ensemble particles is considered from the view point of uncertainty relations of Robertson-Schrödinger type on the examples of the stochastic image of quantum mechanical canonical coherent and squeezed states.

### MSC:

 81Q65 Alternative quantum mechanics (including hidden variables, etc.) 81R30 Coherent states 81P20 Stochastic mechanics (including stochastic electrodynamics) 35Q40 PDEs in connection with quantum mechanics