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TMF, 2016, Volume 188, Number 1, Pages 76–84 (Mi tmf9014)  

This article is cited in 3 scientific papers (total in 3 papers)

Wigner function of a relativistic particle in a time-dependent linear potential

Sh. M. Nagiyev

Institute of Physics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan

Abstract: We construct phase-space representations for a relativistic particle in both a constant and a time-dependent linear potential. We obtain explicit expressions for the Wigner distribution functions for these systems and find the correct nonrelativistic limit and free-particle limit for these functions. We derive the relativistic dynamical equation governing the time development of the Wigner distribution function and relativistic equation for the Wigner distribution function of stationary states and also calculate the amplitudes of transitions between energy states.

Keywords: relativistic particle, linear potential, Wigner function, dynamical equation

Funding Agency
This research is supported by the Science Development Foundation under the President of the Republic of Azerbaijan (Research Grant No. EIF-2012-2(6)-39/08/1).


DOI: https://doi.org/10.4213/tmf9014

Full text: PDF file (375 kB)
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English version:
Theoretical and Mathematical Physics, 2016, 188:1, 1030–1037

Bibliographic databases:

PACS: 02.30.Gp, 03.65.Pm, 03.65.Vf
Received: 23.07.2015

Citation: Sh. M. Nagiyev, “Wigner function of a relativistic particle in a time-dependent linear potential”, TMF, 188:1 (2016), 76–84; Theoret. and Math. Phys., 188:1 (2016), 1030–1037

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf9014
  • https://doi.org/10.4213/tmf9014
  • http://mi.mathnet.ru/eng/tmf/v188/i1/p76

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Sh. M. Nagiyev, “Using the evolution operator method to describe a particle in a homogeneous alternating field”, Theoret. and Math. Phys., 194:2 (2018), 313–327  mathnet  crossref  crossref  adsnasa  isi  elib
    2. Sh. M. Nagiyev, A. I. Akhmedov, “Time evolution of quadratic quantum systems: Evolution operators, propagators, and invariants”, Theoret. and Math. Phys., 198:3 (2019), 392–411  mathnet  crossref  crossref  adsnasa  isi  elib
    3. Nagiyev Sh.M. Ahmadov A.I. Tarverdiyeva V.A. Amirova Sh.A., “Regarding Nonstationary Quadratic Quantum Systems”, Russ. Phys. J., 61:12 (2019), 2173–2187  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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