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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2011, Issue 1, Pages 99–104
(Mi vuu210)
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This article is cited in 5 scientific papers (total in 5 papers)
MATHEMATICS
The Lippmann–Schwinger equation for quantum wires
T. S. Tinyukova Udmurt State University, Izhevsk, Russia
Abstract:
We consider the discrete Schrodinger operator with a potential of a special form defined on a graph whose nodes lie on the union of two intersected straight lines. We prove that there exist unique quasi-levels (eigenvalues or resonances) in the neighborhoods of the point $\pm2$ (these points consist a boundary of the essential spectrum). The asymptotic formulae for quasi-levels are obtained. We find the conditions for the coefficient of reflection is equal to zero.
Keywords:
eigenvalue, resonance, discrete Lippmann–Schwinger equation.
Received: 01.09.2010
Citation:
T. S. Tinyukova, “The Lippmann–Schwinger equation for quantum wires”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 1, 99–104
Linking options:
https://www.mathnet.ru/eng/vuu210 https://www.mathnet.ru/eng/vuu/y2011/i1/p99
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Abstract page: | 521 | Full-text PDF : | 249 | References: | 55 | First page: | 1 |
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