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 Fundam. Prikl. Mat., 2006, Volume 12, Issue 6, Pages 157–174 (Mi fpm995)

On the dynamics of quantum states generated by the Cauchy problem for the Schrödinger equation with degeneration on the half-line

V. Zh. Sakbaev

Moscow Institute of Physics and Technology

Abstract: The paper considers the Cauchy problem for the Schrödinger equation with an operator degenerate on the half-line and the family of regularized Cauchy problems with uniformly elliptic operators whose solutions approximate the solution of the degenerate problem. The author studies the strong and weak convergence of the regularized problems and the convergence of values of quadratic forms of bounded operators on solutions of the regularized problems when the regularization parameter tends to zero.

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English version:
Journal of Mathematical Sciences (New York), 2008, 151:1, 2741–2753

Bibliographic databases:

UDC: 517.946

Citation: V. Zh. Sakbaev, “On the dynamics of quantum states generated by the Cauchy problem for the Schrödinger equation with degeneration on the half-line”, Fundam. Prikl. Mat., 12:6 (2006), 157–174; J. Math. Sci., 151:1 (2008), 2741–2753

Citation in format AMSBIB
\Bibitem{Sak06} \by V.~Zh.~Sakbaev \paper On the dynamics of quantum states generated by the Cauchy problem for the Schr\"odinger equation with degeneration on the half-line \jour Fundam. Prikl. Mat. \yr 2006 \vol 12 \issue 6 \pages 157--174 \mathnet{http://mi.mathnet.ru/fpm995} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2314137} \zmath{https://zbmath.org/?q=an:1151.35417} \elib{http://elibrary.ru/item.asp?id=11143813} \transl \jour J. Math. Sci. \yr 2008 \vol 151 \issue 1 \pages 2741--2753 \crossref{https://doi.org/10.1007/s10948-008-0170-1} \elib{http://elibrary.ru/item.asp?id=13590882} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42449114533} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. Zh. Sakbaev, “Cauchy problem for degenerating linear differential equations and averaging of approximating regularizations”, Journal of Mathematical Sciences, 213:3 (2016), 287–459
2. L. S. Efremova, V. Zh. Sakbaev, “Notion of blowup of the solution set of differential equations and averaging of random semigroups”, Theoret. and Math. Phys., 185:2 (2015), 1582–1598
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