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Teoreticheskaya i Matematicheskaya Fizika, 2002, Volume 131, Number 2, Pages 231–243
DOI: https://doi.org/10.4213/tmf327
(Mi tmf327)
 

This article is cited in 20 scientific papers (total in 20 papers)

Distribution Functions in Quantum Mechanics and Wigner Functions

L. S. Kuz'menkova, S. G. Maksimovb

a M. V. Lomonosov Moscow State University, Faculty of Physics
b Instituto Tecnologico de Morelia
References:
Abstract: We formulate and solve the problem of finding a distribution function $F(\mathbf r,\mathbf p,t)$ such that calculating statistical averages leads to the same local values of the number of particles, the momentum, and the energy as those in quantum mechanics. The method is based on the quantum mechanical definition of the probability density not limited by the number of particles in the system. The obtained distribution function coincides with the Wigner function only for spatially homogeneous systems. We obtain the chain of Bogoliubov equations, the Liouville equation for quantum distribution functions with an arbitrary number of particles in the system, the quantum kinetic equation with a self-consistent electromagnetic field, and the general expression for the dielectric permittivity tensor of the electron component of the plasma. In addition to the known physical effects that determine the dispersion of longitudinal and transverse waves in plasma, the latter tensor contains a contribution from the exchange Coulomb correlations significant for dense systems.
Received: 29.03.2001
Revised: 16.10.2001
English version:
Theoretical and Mathematical Physics, 2002, Volume 131, Issue 2, Pages 641–650
DOI: https://doi.org/10.1023/A:1015472714896
Bibliographic databases:
Language: Russian
Citation: L. S. Kuz'menkov, S. G. Maksimov, “Distribution Functions in Quantum Mechanics and Wigner Functions”, TMF, 131:2 (2002), 231–243; Theoret. and Math. Phys., 131:2 (2002), 641–650
Citation in format AMSBIB
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\by L.~S.~Kuz'menkov, S.~G.~Maksimov
\paper Distribution Functions in Quantum Mechanics and Wigner Functions
\jour TMF
\yr 2002
\vol 131
\issue 2
\pages 231--243
\mathnet{http://mi.mathnet.ru/tmf327}
\crossref{https://doi.org/10.4213/tmf327}
\zmath{https://zbmath.org/?q=an:1038.81040}
\transl
\jour Theoret. and Math. Phys.
\yr 2002
\vol 131
\issue 2
\pages 641--650
\crossref{https://doi.org/10.1023/A:1015472714896}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000176246100006}
Linking options:
  • https://www.mathnet.ru/eng/tmf327
  • https://doi.org/10.4213/tmf327
  • https://www.mathnet.ru/eng/tmf/v131/i2/p231
  • This publication is cited in the following 20 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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    References:59
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