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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.

Keywords

Cite

@article{arxiv.2402.07409,
  title  = {Splitting Quantum Graphs},
  author = {Nathaniel Smith and Alim Sukhtayev},
  journal= {arXiv preprint arXiv:2402.07409},
  year   = {2024}
}

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6 figures