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Mathematics of the USSR-Sbornik, 1981, Volume 39, Issue 2, Pages 169–188
DOI: https://doi.org/10.1070/SM1981v039n02ABEH001480 (Mi sm2499) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On the asymptotic behavior of solutions of the time-dependent Schrödinger equation

D. R. Yafaev
English version PDF (1332 kB) Citations (5) Russian version article
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DOI: https://doi.org/10.1070/SM1981v039n02ABEH001480
Abstract: The asymptotics for large time of solutions of an evolution equation with a selfadjoint Hamiltonian $H(t)$ having discrete spectrum are studied. Conditions are found under which the evolution equation has a solution which behaves asymptotically like an eigenfunction of the operator $H(t)$. In application to the Schrödinger differential equation it is shown that “bound states” may exist for an interaction which decays (or grows) sufficiently slowly in time.
Bibliography: 20 titles.
Received: 02.04.1979
Bibliographic databases:
UDC: 517.948.35
MSC: 35J10, 35B40
Language: English
Original paper language: Russian
Citation: D. R. Yafaev, “On the asymptotic behavior of solutions of the time-dependent Schrödinger equation”, Math. USSR-Sb., 39:2 (1981), 169–188
Citation in format AMSBIB
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\by D.~R.~Yafaev
\paper On the asymptotic behavior of solutions of the time-dependent Schr\"odinger equation
\jour Math. USSR-Sb.
\yr 1981
\vol 39
\issue 2
\pages 169--188
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=564348}
\zmath{https://zbmath.org/?q=an:0462.35008|0432.35021}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1981MK40500002}
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  • https://doi.org/10.1070/SM1981v039n02ABEH001480
  • https://www.mathnet.ru/eng/sm/v153/i2/p187
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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