Asymptotics of the bound state induced by delta-interaction supported on a weakly deformed plane

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F18%3A00486792" target="_blank" >RIV/61389005:_____/18:00486792 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/18:00328105
Result on the web
<a href="http://dx.doi.org/10.1063/1.5019931" target="_blank" >http://dx.doi.org/10.1063/1.5019931</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.5019931" target="_blank" >10.1063/1.5019931</a>

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
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Project
<a href="/en/project/GA17-01706S" target="_blank" >GA17-01706S: Mathematical-Physics Models of Novel Materials</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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