Quantum-mechanical models in \(R_ n\) associated with extensions of the energy operator in a Pontryagin space
type: Item
instance of: scholarly article
title: Quantum-mechanical models in \(R_ n\) associated with extensions of the energy operator in a Pontryagin space
zbMATH Open document ID: 0685.46047
DOI: 10.1007/BF01016615
author: Yu. G. Shondin
published in: Theoretical and Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: This paper is concerned with a rigorous mathematical formulation of a quantum-mechanical model of a point interaction with nontrivial angular momentum transfer. The formal expression for such a model is \[ -\Delta +P_{\ell}((1/i)\partial)\delta (x), \] where \(P_{\ell}\) is a harmonic polynomial, homogeneous of degree \(\ell\). The operator to be constructed is a self-adjoint extension of \(H_ 0=-\Delta\) from the subset of functions which vanish in the neighborhood of \(x=0\). The extension is made from this space to a Pontryagin space \(\Pi_{\kappa}\), that is, a space with indefinite metric, having \(\kappa\) negative squares.
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 46C20
Mathematics Subject Classification ID: 81Q10
zbMATH DE Number: 4122641
zbMATH Keywords: rigorous mathematical formulation of a quantum-mechanical model
zbMATH Keywords: of a point interaction with nontrivial angular momentum transfer
zbMATH Keywords: harmonic polynomial
zbMATH Keywords: self-adjoint extension
zbMATH Keywords: Pontryagin space
zbMATH Keywords: indefinite metric
zbMATH Keywords: rigorous mathematical formulation of a quantum-mechanical model of a point interaction with nontrivial angular momentum transfer
MaRDI profile type: Publication
cites work: Q4774569
cites work: Q4743338
cites work: Extension theory of formally normal and symmetric subspaces
cites work: Q5508534
description: scientific article; zbMATH DE number 4122641