Jussi Behrndt, Pavel Exner, Markus Holzmann, Vladimir Lotoreichik
Approximation of Schroedinger operators with $\delta$-interactions supported on hypersurfaces
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ABSTRACT. We show that a Schr\"odinger operator $A_{\delta, lpha}$ with a $\delta$-interaction of strength $lpha$ supported on a bounded or unbounded $C^2$-hypersurface $\Sigma \subset \mathbb{R}^d$, $d\ge 2$,
can be approximated in the norm resolvent sense by a family of Hamiltonians with suitably scaled regular potentials. The differential operator $A_{\delta, lpha}$ with a singular interaction is regarded as a self-adjoint realization of the formal differential expression $-\Delta - lpha \langle \delta_{\Sigma},