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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2002, Issue 3(26), Pages 99–114
(Mi iimi253)
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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 $\lambda \not=0$.
Received: 01.06.2002
Citation:
M. S. Smetanina, “On Scrödinger equation with non-local potential”, Izv. IMI UdGU, 2002, no. 3(26), 99–114
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https://www.mathnet.ru/eng/iimi253 https://www.mathnet.ru/eng/iimi/y2002/i3/p99
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Abstract page: | 344 | Full-text PDF : | 99 | References: | 75 |
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