stability of eigenvalues
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2015 ◽  
Vol 123-124 ◽  
pp. 56-67 ◽  
Author(s):  
Francesca Colasuonno ◽  
Marco Squassina

Author(s):  
Gregory Berkolaiko ◽  
Tracy Weyand

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


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