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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 139, Number 1, Pages 129–144
DOI: https://doi.org/10.4213/tmf47
(Mi tmf47)
 

This article is cited in 6 scientific papers (total in 6 papers)

The Generalized “Position–Momentum” Uncertainty Relation in Quantum Mechanics and in the Theory of Brownian Motion

A. D. Sukhanov

Peoples Friendship University of Russia
Full-text PDF (254 kB) Citations (6)
References:
Abstract: We show that the generalized Schrödinger uncertainty relations have the meaning of fundamental restrictions on the characteristics of the state space in any theory of a probabilistic type. Both quantum mechanics and the theory of Brownian motion for arbitrary time intervals are among these theories. We compare the “position-momentum” uncertainty relation in the theory of Brownian motion and a similar uncertainty relation for a microparticle in the Gaussian wave-packet state. We establish that the two theories are conceptually similar despite a serious distinction between their mathematical apparatus. This similarity manifests itself in alternative regimes such that small times in one theory correspond to large times in the other theory, and vice versa. In each of the theories, an uncontrollable effect of either quantum or thermal type is of crucial importance.
Keywords: quantum mechanics, stochastic mechanics, Heisenberg uncertainty relations, Schrödinger uncertainty relations, Brownian motion, Fokker–Planck equation, Kramers kinetic equation, uncontrollable effect (quantum and thermal).
English version:
Theoretical and Mathematical Physics, 2004, Volume 139, Issue 1, Pages 557–570
DOI: https://doi.org/10.1023/B:TAMP.0000022747.19258.45
Bibliographic databases:
Language: Russian
Citation: A. D. Sukhanov, “The Generalized “Position–Momentum” Uncertainty Relation in Quantum Mechanics and in the Theory of Brownian Motion”, TMF, 139:1 (2004), 129–144; Theoret. and Math. Phys., 139:1 (2004), 557–570
Citation in format AMSBIB
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\paper The Generalized ``Position--Momentum'' Uncertainty Relation in Quantum Mechanics and in the Theory of Brownian Motion
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\transl
\jour Theoret. and Math. Phys.
\yr 2004
\vol 139
\issue 1
\pages 557--570
\crossref{https://doi.org/10.1023/B:TAMP.0000022747.19258.45}
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  • https://www.mathnet.ru/eng/tmf47
  • https://doi.org/10.4213/tmf47
  • https://www.mathnet.ru/eng/tmf/v139/i1/p129
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:1096
    Full-text PDF :336
    References:62
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