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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.07409 |
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| _version_ | 1866909102425243648 |
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| author | Smith, Nathaniel Sukhtayev, Alim |
| author_facet | Smith, Nathaniel Sukhtayev, Alim |
| contents | We derive a counting formula for the eigenvalues of Schrödinger 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07409 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Splitting Quantum Graphs Smith, Nathaniel Sukhtayev, Alim Spectral Theory 34B45, 47A10 We derive a counting formula for the eigenvalues of Schrödinger 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. |
| title | Splitting Quantum Graphs |
| topic | Spectral Theory 34B45, 47A10 |
| url | https://arxiv.org/abs/2402.07409 |