Singular Schrödinger operators as limits of point interaction Hamiltonians
type: Item
instance of: scholarly article
title: Singular Schrödinger operators as limits of point interaction Hamiltonians
zbMATH Open document ID: 0907.35037
DOI: 10.1023/A:1008654423238
published in: Potential Analysis
publication date: 1999-02-15T00:00:00Z
review text: The results of this paper concern the approximation of Schrödinger operators of the form \(H=-\Delta+\mu\) in one and three space dimensions, where \(\mu\) is a finite Radon measure. In dimension one, \(H\) is shown to be the norm resolvent limit of \(-\Delta+\mu_n\) if \(\mu_n\) is a sequence of finite Radon measures weakly converging to \(\mu\). In particular \(H\) may be approximated by operators with smooth potentials as well as by operators with point interactions. In three dimensions a result concerning the approximation with point interactions, similar to the one above, is proved for \(\mu\) belonging to a large but restricted class of finite Radon measures. Applications to concrete examples are given.
reviewed by: M. Griesemer
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 47B80
zbMATH DE Number: 1160071
zbMATH Keywords: generalized Schrödinger operator
zbMATH Keywords: resolvent convergence
zbMATH Keywords: Monte-Carlo methods
author: J. Brasche
author: Rodolfo Figari
author: Alessandro Teta
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1160071