An index theorem for Schrödinger operators on metric graphs. (English) Zbl 1457.58014
Abdul-Rahman, Houssam (ed.) et al., Analytic trends in mathematical physics. Arizona school of analysis and mathematical physics, University of Arizona, Tucson, AZ, USA, March 5–9, 2018. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 741, 105-119 (2020).
Summary: We show that the spectral flow of a one-parameter family of Schrödinger 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.
For the entire collection see [Zbl 1435.05002].
For the entire collection see [Zbl 1435.05002].
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