Spectral flow and Levinson's theorem for Schrö dinger operators
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917679169798144 |
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| author | Alexander, Angus Rennie, Adam |
| author_facet | Alexander, Angus Rennie, Adam |
| contents | We use spectral flow to present a new proof of Levinson's theorem for Schrödinger operators on $\mathbb{R}^n$ with smooth compactly supported potential. Our proof is valid in all dimensions and in the presence of resonances. The statement is expressed in terms of the spectral shift function and the ``high energy corrected time delay'' following Guillopé and others. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19571 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral flow and Levinson's theorem for Schrö dinger operators Alexander, Angus Rennie, Adam Mathematical Physics Spectral Theory 47A40, 58J30, 81U20, 81U24 We use spectral flow to present a new proof of Levinson's theorem for Schrödinger operators on $\mathbb{R}^n$ with smooth compactly supported potential. Our proof is valid in all dimensions and in the presence of resonances. The statement is expressed in terms of the spectral shift function and the ``high energy corrected time delay'' following Guillopé and others. |
| title | Spectral flow and Levinson's theorem for Schrö dinger operators |
| topic | Mathematical Physics Spectral Theory 47A40, 58J30, 81U20, 81U24 |
| url | https://arxiv.org/abs/2405.19571 |