Atoms confined by very thin layers

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Atoms confined by very thin layers

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Atoms confined by very thin layers

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GA13-11058S" target="_blank" >GA13-11058S: Spektrální analýza operátorů a její aplikace v kvantové mechanice</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Physics

ISSN

0022-2488

e-ISSN

—

Svazek periodika

55

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

"112105-1"-"112105-17"

Kód UT WoS článku

000345643100012

EID výsledku v databázi Scopus

—