Trace formula and Levinson's theorem as an index pairing in the presence of resonances
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911783857422336 |
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| author | Alexander, Angus |
| author_facet | Alexander, Angus |
| contents | We realise the number of bound states of a Schrödinger operator on $\mathbb{R}^n$ as an index pairing in all dimensions. Expanding on ideas of Guillopé and others, we use high-energy corrections to find representatives of the $K$-theory class of the scattering operator. These representatives allow us to compute the number of bound states using an integral formula involving heat kernel coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15979 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Trace formula and Levinson's theorem as an index pairing in the presence of resonances Alexander, Angus K-Theory and Homology Mathematical Physics Spectral Theory 19K56, 47A40, 81U20, 81U24 We realise the number of bound states of a Schrödinger operator on $\mathbb{R}^n$ as an index pairing in all dimensions. Expanding on ideas of Guillopé and others, we use high-energy corrections to find representatives of the $K$-theory class of the scattering operator. These representatives allow us to compute the number of bound states using an integral formula involving heat kernel coefficients. |
| title | Trace formula and Levinson's theorem as an index pairing in the presence of resonances |
| topic | K-Theory and Homology Mathematical Physics Spectral Theory 19K56, 47A40, 81U20, 81U24 |
| url | https://arxiv.org/abs/2402.15979 |