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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2605.27592 |
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| _version_ | 1866917538020982784 |
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| author | Sutton, Owen Watson, Alexander B. |
| author_facet | Sutton, Owen Watson, Alexander B. |
| contents | We study the semiclassical spectral theory of a one-dimensional Dirac operator describing waves at the interface between topologically distinct media. We derive a modified Bohr-Sommerfeld quantization condition for the squared operator via a systematic formal WKB construction producing approximate eigenpairs. Our result differs from the standard result by the half-integer shift depending on the pseudo-spin index which allows for recovering the topologically protected zero mode. We verify our result for the solvable Pöschl--Teller potential and provide numerical computations confirming the convergence of eigenvalues and eigenfunctions to their WKB approximations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27592 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | WKB Spectral Asymptotics for a One-Dimensional Dirac Operator with a Slowly Varying Mass Profile Sutton, Owen Watson, Alexander B. Mathematical Physics We study the semiclassical spectral theory of a one-dimensional Dirac operator describing waves at the interface between topologically distinct media. We derive a modified Bohr-Sommerfeld quantization condition for the squared operator via a systematic formal WKB construction producing approximate eigenpairs. Our result differs from the standard result by the half-integer shift depending on the pseudo-spin index which allows for recovering the topologically protected zero mode. We verify our result for the solvable Pöschl--Teller potential and provide numerical computations confirming the convergence of eigenvalues and eigenfunctions to their WKB approximations. |
| title | WKB Spectral Asymptotics for a One-Dimensional Dirac Operator with a Slowly Varying Mass Profile |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2605.27592 |