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Izv. IMI UdGU, 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

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 $\lambda \not=0$.

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Received: 01.06.2002

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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    This publication is cited in the following articles:
    1. N. I. Pletnikova, “Ob odnomernom uravnenii Shredingera s nelokalnym potentsialom tipa vozmuschennoi stupenki”, Izv. IMI UdGU, 2004, no. 1(29), 95–108  mathnet
    2. M. S. Smetanina, “Asimptotika urovnei odnomernogo operatora Shredingera s nelokalnym potentsialom”, Izv. IMI UdGU, 2005, no. 1(31), 99–106  mathnet
    3. M. S. Smetanina, “Ob urovnyakh operatora Shredingera s vozmuschennym nelokalnym potentsialom”, Izv. IMI UdGU, 2006, no. 1(35), 98–104  mathnet
    4. M. S. Smetanina, “Asimptotika urovnei operatora Shrëdingera dlya kristallicheskoi plenki s nelokalnym potentsialom”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:4 (2018), 462–473  mathnet  crossref  elib
  • Известия Института математики и информатики Удмуртского государственного университета
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