Convergence of 2D-Schrödinger operators with local scaled short-range interactions to a Hamiltonian with infinitely many δ-point interactions

Jussi Behrndt; Markus Holzmann; Vladimir Lotoreichik

doi:10.1002/pamm.201410482

Convergence of 2D-Schrödinger operators with local scaled short-range interactions to a Hamiltonian with infinitely many δ-point interactions

Jussi Behrndt^*, Markus Holzmann, Vladimir Lotoreichik

^*Corresponding author for this work

Institute of Applied Mathematics (5040)

Research output: Contribution to journal › Conference article

Abstract

We prove, that a Hamiltonian with infinitely many δ-point interactions in the plane can be approximated in the norm resolvent sense by a family of Schrödinger operators with regular, local scaled short-range potentials. Similar well known results from the 1D and the 3D case are complemented thereby

Original language	English
Pages (from-to)	1005-1006
Journal	Proceedings in Applied Mathematics and Mechanics
Volume	14
Issue number	1
DOIs	https://doi.org/10.1002/pamm.201410482
Publication status	Published - 2014
Event	85th Annual Meeting of the International Association of Applied Mathematics and Mechanics: GAMM 2014 - Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany Duration: 10 Mar 2014 → 14 Mar 2014

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Basic - Fundamental (Grundlagenforschung)

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10.1002/pamm.201410482

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@article{6400bd78fa764ceeb6a12a23bd737eb3,

title = "Convergence of 2D-Schr{\"o}dinger operators with local scaled short-range interactions to a Hamiltonian with infinitely many δ-point interactions",

abstract = "We prove, that a Hamiltonian with infinitely many δ-point interactions in the plane can be approximated in the norm resolvent sense by a family of Schr{\"o}dinger operators with regular, local scaled short-range potentials. Similar well known results from the 1D and the 3D case are complemented thereby",

author = "Jussi Behrndt and Markus Holzmann and Vladimir Lotoreichik",

year = "2014",

doi = "10.1002/pamm.201410482",

language = "English",

volume = "14",

pages = "1005--1006",

journal = "Proceedings in Applied Mathematics and Mechanics ",

issn = "1617-7061",

publisher = "Wiley-Blackwell",

number = "1",

note = "85th Annual Meeting of the International Association of Applied Mathematics and Mechanics : GAMM 2014 ; Conference date: 10-03-2014 Through 14-03-2014",

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TY - JOUR

T1 - Convergence of 2D-Schrödinger operators with local scaled short-range interactions to a Hamiltonian with infinitely many δ-point interactions

AU - Behrndt, Jussi

AU - Holzmann, Markus

AU - Lotoreichik, Vladimir

PY - 2014

Y1 - 2014

N2 - We prove, that a Hamiltonian with infinitely many δ-point interactions in the plane can be approximated in the norm resolvent sense by a family of Schrödinger operators with regular, local scaled short-range potentials. Similar well known results from the 1D and the 3D case are complemented thereby

AB - We prove, that a Hamiltonian with infinitely many δ-point interactions in the plane can be approximated in the norm resolvent sense by a family of Schrödinger operators with regular, local scaled short-range potentials. Similar well known results from the 1D and the 3D case are complemented thereby

U2 - 10.1002/pamm.201410482

DO - 10.1002/pamm.201410482

M3 - Conference article

SN - 1617-7061

VL - 14

SP - 1005

EP - 1006

JO - Proceedings in Applied Mathematics and Mechanics

JF - Proceedings in Applied Mathematics and Mechanics

IS - 1

T2 - 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics

Y2 - 10 March 2014 through 14 March 2014

ER -

Convergence of 2D-Schrödinger operators with local scaled short-range interactions to a Hamiltonian with infinitely many δ-point interactions

Abstract

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Treatment code (Nähere Zuordnung)

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