Approximation of Schrodinger operators with delta-interactions supported on hypersurfaces

0475714 - ÚJF 2018 RIV DE eng J - Článek v odborném periodiku
Behrndt, J. - Exner, Pavel - Holzmann, M. - Lotoreichik, Vladimir
Approximation of Schrodinger operators with delta-interactions supported on hypersurfaces.
Mathematische Nachrichten. Roč. 290, 8-9 (2017), s. 1215-1248. ISSN 0025-584X. E-ISSN 1522-2616
Grant CEP: GA ČR(CZ) GA14-06818S
Institucionální podpora: RVO:61389005
Klíčová slova: Schrodinger operators * delta-interactions supported on hypersurfaces * approximation by scaled regular potentials * norm resolvent convergence * spectral convergence
Obor OECD: Pure mathematics
Impakt faktor: 0.843, rok: 2017

We show that a Schrodinger operator A(delta,alpha) with a delta-interaction of strength alpha supported on a bounded or unbounded C-2-hypersurface Sigma subset of R-d, d >= 2, can be approximated in the norm resolvent sense by a family of Hamiltonians with suitably scaled regular potentials. The differential operator A(delta,alpha) with a singular interaction is regarded as a self-adjoint realization of the formal differential expression - Delta - alpha <delta(Sigma),.>delta(Sigma), where alpha : Sigma -> R is an arbitrary bounded measurable function. We discuss also some spectral consequences of this approximation result.
Trvalý link: http://hdl.handle.net/11104/0272359