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.


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