An index theorem for Schr\"odinger operators on metric graphs
Spectral Theory
2018-09-27 v2
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.
Keywords
Cite
@article{arxiv.1809.09344,
title = {An index theorem for Schr\"odinger operators on metric graphs},
author = {Yuri Latushkin and Selim Sukhtaiev},
journal= {arXiv preprint arXiv:1809.09344},
year = {2018}
}