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Nanosystems: Physics, Chemistry, Mathematics, 2021, Volume 12, Issue 5, Pages 549–552
DOI: https://doi.org/10.17586/2220-8054-2021-12-5-549-552 (Mi nano1049) 		 
MATHEMATICS

Bound states for Laplacian perturbed by varying potential supportedby line in $\mathbb{R}^3$

A. S. Bagmutov

ITMO University, Kronverkskiy, 49, Saint Petersburg, 197101, Russia
Full-text PDF (222 kB)
DOI: https://doi.org/10.17586/2220-8054-2021-12-5-549-552
Abstract: We investigate a system with attracting $\delta$-potential located along a straight line in 3D. It has constant intensity, except for a local region. We prove the existence of discrete spectrum and construct an upper bound on the number of bound states, using Birman–Schwinger method.
Keywords: operator extension theory, singular potential, spectrum.
Funding agency Grant number
Russian Foundation for Basic Research 20-31-90050
The reported study was funded by RFBR, project number 20-31-90050.
Received: 17.07.2021
Revised: 10.10.2021
Bibliographic databases:
Document Type: Article
Language: English
Citation: A. S. Bagmutov, “Bound states for Laplacian perturbed by varying potential supportedby line in $\mathbb{R}^3$”, Nanosystems: Physics, Chemistry, Mathematics, 12:5 (2021), 549–552
Citation in format AMSBIB
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\by A.~S.~Bagmutov
\paper Bound states for Laplacian perturbed by varying potential supportedby line in $\mathbb{R}^3$
\jour Nanosystems: Physics, Chemistry, Mathematics
\yr 2021
\vol 12
\issue 5
\pages 549--552
\mathnet{http://mi.mathnet.ru/nano1049}
\crossref{https://doi.org/10.17586/2220-8054-2021-12-5-549-552}
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\elib{https://elibrary.ru/item.asp?id=47159874}
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