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Pis'ma v Zh. Èksper. Teoret. Fiz., 2017, Volume 105, Issue 9, Pages 565–569 (Mi jetpl5262)  

This article is cited in 4 scientific papers (total in 4 papers)

METHODS OF THEORETICAL PHYSICS

Quantum-Mechanical generalization of the Thomas–Fermi model

A. V. Chaplik

Rzhanov Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

Abstract: The interaction between particles in the mean-field approximation of the many-body theory is often taken into account with the use of the semiclassical description of the particle motion. However, quantization of a part of the degrees of freedom becomes essential in certain cases. In this work, two such cases where nonlinear wave equations appear have been considered: electrons in a quantum well and excitons in a trap. In the case of indirect excitons in an annular trap, the one-dimensional Gross–Pitaevskii equation permits an analytical solution and it turns out that there can be no bound state in a one-dimensional symmetric potential well. This makes the problem qualitatively different from a similar one-body problem. In the case of electrons in a quantum well, the nonlinear integro-differential equation does not have an exact solution and the allowed energy levels have been found by the direct variational method.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-02-00565_


DOI: https://doi.org/10.7868/S0370274X17090107

Full text: PDF file (165 kB)
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English version:
Journal of Experimental and Theoretical Physics Letters, 2017, 105:9, 601–605

Bibliographic databases:

Document Type: Article
Received: 24.03.2017

Citation: A. V. Chaplik, “Quantum-Mechanical generalization of the Thomas–Fermi model”, Pis'ma v Zh. Èksper. Teoret. Fiz., 105:9 (2017), 565–569; JETP Letters, 105:9 (2017), 601–605

Citation in format AMSBIB
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\paper Quantum-Mechanical generalization of the Thomas--Fermi model
\jour Pis'ma v Zh. \`Eksper. Teoret. Fiz.
\yr 2017
\vol 105
\issue 9
\pages 565--569
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\crossref{https://doi.org/10.7868/S0370274X17090107}
\elib{http://elibrary.ru/item.asp?id=29276531}
\transl
\jour JETP Letters
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\vol 105
\issue 9
\pages 601--605
\crossref{https://doi.org/10.1134/S0021364017090089}
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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. S. E. Savotchenko, “Inhomogeneous states in a nonlinear self-focusing medium generated by a nonlinear defect”, JETP Letters, 107:8 (2018), 455–457  mathnet  crossref  crossref  isi  elib
    2. Savotchenko S.E., “Stationary States Near the Interface With Anharmonic Properties Between Linear and Nonlinear Defocusing Media”, Solid State Commun., 283 (2018), 1–8  crossref  mathscinet  isi  scopus
    3. Savotchenko S.E., “Localization on the Interface With Nonlinear Response Between Linear and Nonlinear Focusing Media”, Surf. Interfaces, 13 (2018), 157–162  crossref  isi  scopus
    4. Savotchenko S.E., “The Field Blocking on the Interface With Nonlinear Response Between Nonlinear Focusing Media”, Turk. J. Phys., 42:6 (2018), 721–736  crossref  isi  scopus
  •       Pis'ma v Zhurnal ksperimental'noi i Teoreticheskoi Fiziki
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