Boundary triples for Schrodinger operators with singular interactions on hypersurfaces

0466591 - ÚJF 2017 RIV RU eng J - Journal Article
Behrndt, J. - Langer, M. - Lotoreichik, Vladimir
Boundary triples for Schrodinger operators with singular interactions on hypersurfaces.
Nanosystems: Physics, Chemistry, Mathematics. Roč. 7, č. 2 (2016), s. 290-302. ISSN 2220-8054
R&D Projects: GA ČR(CZ) GA14-06818S
Institutional support: RVO:61389005
Keywords : boundary triple * Weyl function * Schrodinger operator * singular potential * delta-interaction * hypersurface
Subject RIV: BE - Theoretical Physics

The 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).
Permanent Link: http://hdl.handle.net/11104/0264855