# Approximations of quantum-graph vertex couplings by singularly scaled potentials

@article{Exner2013ApproximationsOQ, title={Approximations of quantum-graph vertex couplings by singularly scaled potentials}, author={Pavel Exner and Stepan S. Manko}, journal={Journal of Physics A}, year={2013}, volume={46}, pages={345202} }

We investigate the limit properties of a family of Schrodinger operators of the form acting on n-edge star graphs with the Kirchhoff interface conditions at the vertex. Here the real-valued potential Q has compact support and λ( · ) is analytic around e = 0 with λ(0) = 1. We show that if the operator has a zero-energy resonance of order m for e = 1 and λ(1) = 1, in the limit e → 0 one obtains the Laplacian with a vertex coupling depending on parameters. We prove the norm-resolvent convergence… CONTINUE READING

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