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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2002, Issue 3(26), Pages 99–114 (Mi iimi253)  

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

On Scrödinger equation with non-local potential

M. S. Smetanina

Udmurt State University, Izhevsk
References:
Abstract: We consider the Schrödinger operator of the form $H=-d^2/dx^2+V$ acting in $L^2({\mathbf R})$ where $V=\varepsilon W(x)+\lambda(\cdot,\phi _0)\phi_0$ is non-local potential. It is proved, that the unique level (i. e. eigenvalue or resonance of the operator $H$) exists for $V=\lambda(\cdot,\phi_0)\phi_0$ for all sufficiently small $\lambda$. We investigate the asymptotic behaviour of level for a small $\lambda$. We prove that there are no levels for $V=\varepsilon W(x)+\lambda(\cdot,\phi_0)\phi_0$ for all sufficiently small $\varepsilon$, if $\lambda \not=0$.
Received: 01.06.2002
Document Type: Article
Language: Russian
Citation: M. S. Smetanina, “On Scrödinger equation with non-local potential”, Izv. IMI UdGU, 2002, no. 3(26), 99–114
Citation in format AMSBIB
\Bibitem{Sme02}
\by M.~S.~Smetanina
\paper On Scr\"odinger equation with non-local potential
\jour Izv. IMI UdGU
\yr 2002
\issue 3(26)
\pages 99--114
\mathnet{http://mi.mathnet.ru/iimi253}
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  • https://www.mathnet.ru/eng/iimi253
  • https://www.mathnet.ru/eng/iimi/y2002/i3/p99
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Института математики и информатики Удмуртского государственного университета
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