On the Uncertainty Relations in Stochastic Mechanics

Details On the Uncertainty Relations in Stochastic Mechanics On the Uncertainty Relations in Stochastic Mechanics

2009-02-23

arxiv.org/abs/0902.3880v4

J. Geometry and Symmetry in Physics (JGSP) 16 (2009) 57-75

Physics

Quantum Physics

Latex, 15 pages, no figures. The revised version: some formulae corrected, several new references added, text amended accordin

Scientific paper

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 admiting an aditional 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 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 - Schroedinger type on the examples of the stochastic image of quantum mechanical canonical coherent and squeezed states.

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