Approximation of magnetic Schrödinger operators with $\hat{I}´$-interactions supported on networks

Abstract

This paper deals with the approximation of a magnetic Schrödinger operator with a singular $\hat{I}´$-potential that is formally given by $(i\nabla +A{)}^2+Q+\hat{I}\pm \hat{I}{´}_{\hat{I}}\pounds$ by Schrödinger operators with regular potentials in the norm resolvent sense. This is done for $\hat{I}\pounds$ being the finite union of $C^2$-hypersurfaces, for coefficients $A$, $Q$, and $\hat{I}\pm$ under almost minimal assumptions such that the associated quadratic forms are closed and sectorial, and $Q$ and $\hat{I}\pm$ are allowed to be complex-valued functions. In particular, $\hat{I}\pounds$ can be a graph in ${\mathbb{R}}^2$ or the boundary of a piecewise $C^2$-domain. Moreover, spectral implications of the mentioned convergence result are discussed.

21 pages; revised version