Atoms confined by very thin layers
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F14%3A00222327" target="_blank" >RIV/68407700:21340/14:00222327 - isvavai.cz</a>
Result on the web
<a href="http://scitation.aip.org/content/aip/journal/jmp/55/11/10.1063/1.4901560" target="_blank" >http://scitation.aip.org/content/aip/journal/jmp/55/11/10.1063/1.4901560</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.4901560" target="_blank" >10.1063/1.4901560</a>
Alternative languages
Result language
angličtina
Original language name
Atoms confined by very thin layers
Original language description
The Hamiltonian of an atom with N electrons and a fixed nucleus of infinite mass between two parallel planes is considered in the limit when the distance a between the planes tends to zero. We show that this Hamiltonian converges in the norm resolvent sense to a Schrödinger operator acting effectively in L^2(R^2N) whose potential part depends on a. Moreover, we prove that after an appropriate regularization this Schrödinger operator tends, again in the norm resolvent sense, to the Hamiltonian of a two-dimensional atom (with the three-dimensional Coulomb potential-one over distance) as a->0. This makes possible to locate the discrete spectrum of the full Hamiltonian once we know the spectrum of the latter one. Our results also provide a mathematical justification for the interest in the two-dimensional atoms with the three-dimensional Coulomb potential.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA13-11058S" target="_blank" >GA13-11058S: Spectral analysis of operators and its applications in quantum mechanics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2014
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
55
Issue of the periodical within the volume
11
Country of publishing house
US - UNITED STATES
Number of pages
17
Pages from-to
"112105-1"-"112105-17"
UT code for WoS article
000345643100012
EID of the result in the Scopus database
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