An index theorem for Schrödinger operators on metric graphs

Published 25 Sep 2018 in math.SP | (1809.09344v2)

Abstract: We show that the spectral flow of a one-parameter family of Schr\"odinger operators on a metric graph is equal to the Maslov index of a path of Lagrangian subspaces describing the vertex conditions. In addition, we derive an Hadamard-type formula for the derivatives of the eigenvalue curves via the Maslov crossing form.

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