Splitting Quantum Graphs
Spectral Theory
2024-02-13 v1
Abstract
We derive a counting formula for the eigenvalues of Schr\"odinger operators with self-adjoint boundary conditions on quantum star graphs. More specifically, we develop techniques using Evans functions to reduce full quantum graph eigenvalue problems into smaller subgraph eigenvalue problems. These methods provide a simple way to calculate the spectra of operators with localized potentials.
Cite
@article{arxiv.2402.07409,
title = {Splitting Quantum Graphs},
author = {Nathaniel Smith and Alim Sukhtayev},
journal= {arXiv preprint arXiv:2402.07409},
year = {2024}
}
Comments
6 figures