Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions Academic Article uri icon


  • We prove an analogue of the magnetic nodal theorem on quantum graphs: the number of zeros of the nth eigenfunction of the Schrödinger operator on a quantum graph is related to the stability of the nth eigenvalue of the perturbation of the operator by magnetic potential. More precisely, we consider the nth eigenvalue as a function of the magnetic perturbation and show that its Morse index at zero magnetic field is equal to φ - (n-1).

author list (cited authors)

  • Berkolaiko, G., & Weyand, T.

complete list of authors

  • Berkolaiko, Gregory||Weyand, Tracy

publication date

  • January 1, 2014 11:11 AM