What question did this study set out to answer?

The research aims to approximate magnetic Schrödinger operators with delta-potentials using regular potentials.

March 2, 2026Open Access

Approximation of magnetic Schrödinger operators with -interactions supported on networks

Key Points

The research aims to approximate magnetic Schrödinger operators with delta-potentials using regular potentials.
Approximation in the norm resolvent sense.
Consideration of delta-interactions supported on finite unions of C^2 hypersurfaces.
Examination of coefficients A, Q, and alpha under minimal assumptions.
Convergence results for the approximation are established.
Discussion of spectral implications resulting from the convergence.
Delta-interactions can be represented on graphs in R^2 or boundaries of piecewise C^2 domains.

Abstract

Abstract This paper deals with the approximation of a magnetic Schrödinger operator with a singular δ -potential that is formally given by (i + A) ² + Q + _ (i ∇ + A) 2 + Q + α δ Σ by Schrödinger operators with regular potentials in the norm resolvent sense. This is done for Σ being the finite union of C² C 2 -hypersurfaces, for coefficients A, Q, and α under almost minimal assumptions such that the associated quadratic forms are closed and sectorial, and Q and α are allowed to be complex-valued functions. In particular, Σ can be a graph in R² R 2 or the boundary of a piecewise C² C 2 -domain. Moreover, spectral implications of the mentioned convergence result are discussed.

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