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We show that a Schrödinger operator    A   δ  ,  αwith 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  ,  αwith 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.

Approximation of Schrödinger operators with δ‐interactions supported on hypersurfaces