Asymptotics of the bound state induced by delta-interaction supported on a weakly deformed plane
Result description
In this paper, we consider the three-dimensional Schrodinger operator with a delta-interaction of strength alpha > 0 supported on an unbounded surface parametrized by the mapping R-2 (sic) x bar right arrow (x, beta f (x)), where beta is an element of [0, infinity) and f : R-2 -> R, f not equivalent to 0, is a C-2-smooth, compactly supported function. The surface supporting the interaction can be viewed as a local deformation of the plane. It is known that the essential spectrum of this Schrodinger operator coincides with [- 1/4 alpha(2), +infinity). We prove that for all sufficiently small beta > 0, its discrete spectrum is non-empty and consists of a unique simple eigenvalue. Moreover, we obtain an asymptotic expansion of this eigenvalue in the limit beta -> 0+. In particular, this eigenvalue tends to -1/4 alpha(2) exponentially fast as beta -> 0+.
Keywords
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/68407700:21340/18:00328105
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Asymptotics of the bound state induced by delta-interaction supported on a weakly deformed plane
Original language description
In this paper, we consider the three-dimensional Schrodinger operator with a delta-interaction of strength alpha > 0 supported on an unbounded surface parametrized by the mapping R-2 (sic) x bar right arrow (x, beta f (x)), where beta is an element of [0, infinity) and f : R-2 -> R, f not equivalent to 0, is a C-2-smooth, compactly supported function. The surface supporting the interaction can be viewed as a local deformation of the plane. It is known that the essential spectrum of this Schrodinger operator coincides with [- 1/4 alpha(2), +infinity). We prove that for all sufficiently small beta > 0, its discrete spectrum is non-empty and consists of a unique simple eigenvalue. Moreover, we obtain an asymptotic expansion of this eigenvalue in the limit beta -> 0+. In particular, this eigenvalue tends to -1/4 alpha(2) exponentially fast as beta -> 0+.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Result continuities
Project
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Physics
ISSN
0022-2488
e-ISSN
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Volume of the periodical
59
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
17
Pages from-to
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UT code for WoS article
000424017000039
EID of the result in the Scopus database
2-s2.0-85040712425
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Year of implementation
2018