Open Access
2009 On the Uncertainty Relations in Stochastic Mechanics
Dimitar A. Trifonov, Blagovest A. Nikolov, Ivaïlo M. Mladenov
J. Geom. Symmetry Phys. 16: 57-75 (2009). DOI: 10.7546/jgsp-16-2009-57-75


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 - Schrödinger type on the examples of the stochastic image of quantum mechanical canonical coherent and squeezed states.


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Dimitar A. Trifonov. Blagovest A. Nikolov. Ivaïlo M. Mladenov. "On the Uncertainty Relations in Stochastic Mechanics." J. Geom. Symmetry Phys. 16 57 - 75, 2009.


Published: 2009
First available in Project Euclid: 24 May 2017

zbMATH: 1193.81039
MathSciNet: MR2643223
Digital Object Identifier: 10.7546/jgsp-16-2009-57-75

Rights: Copyright © 2009 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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