Boundary triples for Schrödinger operators with singular interactions on hypersurfaces

Jussi Behrndt*, Matthias Langer, Vladimir Lotoreichik

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

he self-adjoint Schrodinger operator A(delta, alpha) with a delta-interaction of constant strength alpha supported on a compact smooth hypersurface C is viewed as a self-adjoint extension of a natural underlying symmetric operator S in L-2 (R-n). The aim of this note is to construct a boundary triple for S* and a self-adjoint parameter Theta(delta, alpha) in the boundary space L-2 (C) such that A(delta, alpha) corresponds to the boundary condition induced by Theta(delta, alpha). As a consequence, the well-developed theory of boundary triples and their Weyl functions can be applied. This leads, in particular, to a Krein-type resolvent formula and a description of the spectrum of A(delta, alpha) in terms of the Weyl function and Theta(delta, alpha).
Original languageEnglish
Pages (from-to)290-302
JournalNanosystems = Nanosistemy: Physics, Chemistry, Mathematics
Volume7
Issue number2
DOIs
Publication statusPublished - 2016

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