Approximation of Schrödinger operators with δ‐interactions supported on hypersurfaces. Issue 8 (22nd September 2016) - Behrndt, Jussi; Exner, Pavel; Holzmann, Markus; Lotoreichik, Vladimir
Abstract : We show that a Schrödinger operator A δ, α with a δ‐interaction of strength α supported on a bounded or unbounded C 2 ‐hypersurface Σ ⊂ 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 δ, α with a singular interaction is regarded as a self‐adjoint realization of the formal differential expression − Δ − α ⟨ δ Σ, · ⟩ δ Σ, where α : Σ → R is an arbitrary bounded measurable function. We discuss also some spectral consequences of this approximation result.