15-120 Jussi Behrndt, Pavel Exner, Markus Holzmann, Vladimir Lotoreichik

Approximation of Schroedinger operators with $\delta$-interactions supported on hypersurfaces (616K, pdf) Dec 29, 15

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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},

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