Approximation of Schrödinger operators with δ-interactions sup- ported on hypersurfaces
نویسندگان
چکیده
We show that a Schrödinger operator Aδ,α with a δ-interaction of strength α supported on a bounded or unbounded C-hypersurface Σ ⊂ R, d ≥ 2, can be approximated in the norm resolvent sense by a family of Hamiltonians with suitably scaled regular potentials. The differential operator Aδ,α with a singular interaction is regarded as a self-adjoint realization of the formal differential expression −∆ − α〈δΣ, ·〉δΣ, where α : Σ → R is an arbitrary bounded measurable function. We discuss also some spectral consequences of this approximation result.
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