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Matematicheskie Zametki, 2022, Volume 112, Issue 5, Pages 644–664
DOI: https://doi.org/10.4213/mzm13670 (Mi mzm13670) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On Expansions in the Exact and Asymptotic Eigenfunctions of the One-Dimensional Schrödinger Operator

A. Yu. Anikina, S. Yu. Dobrokhotova, A. A. Shkalikovbc

a Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
b Lomonosov Moscow State University
c Moscow Center for Fundamental and Applied Mathematics
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DOI: https://doi.org/10.4213/mzm13670
Abstract: The one-dimensional Schrödinger operator with potential growing at infinity and with a semiclassical small parameter is considered. We obtain estimates via powers of the small parameter for the remainder in the expansion of smooth sufficiently rapidly decaying functions in the exact and asymptotic eigenfunctions. For the asymptotic eigenfunctions, we use a global representation in the form of an Airy function.
Keywords: eigenfunction, asymptotic eigenfunction, Schrödinger operator, semiclassical asymptotics.
Funding agency Grant number
Russian Science Foundation 20-11-20261
Ministry of Science and Higher Education of the Russian Federation АААА-А20-120011690131-7
The research in Sec. 3 was supported by the Russian Science Foundation under grant 20-11-20261, and that in Sec. 4 was carried out under the Government program (contract no. AAAA-A20-120011690131-7).
Received: 19.07.2022
English version:
Mathematical Notes, 2022, Volume 112, Issue 5, Pages 623–641
DOI: https://doi.org/10.1134/S0001434622110013
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: A. Yu. Anikin, S. Yu. Dobrokhotov, A. A. Shkalikov, “On Expansions in the Exact and Asymptotic Eigenfunctions of the One-Dimensional Schrödinger Operator”, Mat. Zametki, 112:5 (2022), 644–664; Math. Notes, 112:5 (2022), 623–641
Citation in format AMSBIB
\Bibitem{AniDobShk22}
\by A.~Yu.~Anikin, S.~Yu.~Dobrokhotov, A.~A.~Shkalikov
\paper On Expansions in the Exact and Asymptotic Eigenfunctions of the One-Dimensional Schr\"odinger Operator
\jour Mat. Zametki
\yr 2022
\vol 112
\issue 5
\pages 644--664
\mathnet{http://mi.mathnet.ru/mzm13670}
\crossref{https://doi.org/10.4213/mzm13670}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4538796}
\transl
\jour Math. Notes
\yr 2022
\vol 112
\issue 5
\pages 623--641
\crossref{https://doi.org/10.1134/S0001434622110013}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85145038493}
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    • This publication is cited in the following 1 articles:
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