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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 4, Pages 683–699 (Mi zvmmf488)  
This article is cited in 13 scientific papers (total in 13 papers)

Set-valued mappings specified by regularization of the Schrödinger equation with degeneration

V. Zh. Sakbaev

Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia
Full-text PDF (2445 kB) Citations (13)
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Abstract: The Cauchy problem for the Schrödinger equation with an operator degenerating on a half-line and a family of regularized Cauchy problems with uniformly elliptic operators, whose solutions approximate the solution to the degenerate problem, are considered. A set-valued mapping is investigated that takes a bounded operator to a set of partial limits of values of its quadratic form on solutions of the regularized problems when the regularization parameter tends to zero. The dynamics of quantum states are determined by applying an averaging procedure to the set-valued mapping.
Key words: degenerating operator, quantum state, set-valued mapping, finitely additive measure.
Received: 07.12.2004
Revised: 20.02.2005
English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 4, Pages 651–665
DOI: https://doi.org/10.1134/S0965542506040117
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: V. Zh. Sakbaev, “Set-valued mappings specified by regularization of the Schrödinger equation with degeneration”, Zh. Vychisl. Mat. Mat. Fiz., 46:4 (2006), 683–699; Comput. Math. Math. Phys., 46:4 (2006), 651–665
Citation in format AMSBIB
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\by V.~Zh.~Sakbaev
\paper Set-valued mappings specified by regularization of the Schr\"odinger equation with degeneration
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\issue 4
\pages 683--699
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\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 4
\pages 651--665
\crossref{https://doi.org/10.1134/S0965542506040117}
\elib{https://elibrary.ru/item.asp?id=13517234}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746032905}
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    Full-text PDF :136
    References:64
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