Approximations of quantum-graph vertex couplings by singularly scaled potentials

  title={Approximations of quantum-graph vertex couplings by singularly scaled potentials},
  author={Pavel Exner and Stepan S. Manko},
  journal={Journal of Physics A},
  • Pavel Exner, Stepan S. Manko
  • Published 2013
  • Physics, Mathematics
  • Journal of Physics A
  • 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