Extended Ehrenfest theorem with radiative corrections

A set of basic evolution equations for the mean values of dynamical variables is obtained from the Fokker-Planck equation applied to the general problem of a particle subject to a random force. The specific case of stochastic electrodynamics is then considered, in which the random force is due to th...

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Bibliographic Details
Published in:Physica scripta 2015-10, Vol.T165 (1), p.14004
Main Authors: de la Peña, L, Cetto, A M, Valdés-Hernández, A
Format: Article
Language:English
Subjects:
Ehrenfest theorem
Fokker-Planck equation
foundations of quantum mechanics
radiative corrections
stochastic electrodynamics
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Summary:A set of basic evolution equations for the mean values of dynamical variables is obtained from the Fokker-Planck equation applied to the general problem of a particle subject to a random force. The specific case of stochastic electrodynamics is then considered, in which the random force is due to the zero-point radiation field. Elsewhere it has been shown that when this system reaches a state of energy balance, it becomes controlled by an equation identical to Schrödinger's, if the radiationless approximation is made. The Fokker-Planck equation was shown to lead to the Ehrenfest theorem under such an approximation. Here we show that when the radiative terms are not neglected, an extended form of the Ehrenfest equation is obtained, from which follow, among others, the correct formulas for the atomic lifetimes and the (nonrelativistic) Lamb shift.
ISSN:0031-8949
1402-4896
DOI:10.1088/0031-8949/2015/T165/014004