On Explicit Estimations for the Bloch Eigenvalues of the One-dimensional Schrödinger Operator and the Kronig-Penney Model
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913654900785152 |
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| author | Nur, Cemile Veliev, Oktay |
| author_facet | Nur, Cemile Veliev, Oktay |
| contents | In this paper, we consider the small and large eigenvalues of the one-dimensional Schrödinger operator L(q) with a periodic, real and locally integrable potential q. First we explicitly write out the first and second terms of the asymptotic formulas for the large periodic and antiperiodic eigenvalues and illustrate these formulas for the Kronig-Penney model. Then we give estimates for the small periodic and antiperiodic eigenvalues and for the length of the first gaps in the case of the Kronig-Penney model. Moreover, we give error estimations and present a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Explicit Estimations for the Bloch Eigenvalues of the One-dimensional Schrödinger Operator and the Kronig-Penney Model Nur, Cemile Veliev, Oktay Spectral Theory Mathematical Physics 34L20, 47E05 In this paper, we consider the small and large eigenvalues of the one-dimensional Schrödinger operator L(q) with a periodic, real and locally integrable potential q. First we explicitly write out the first and second terms of the asymptotic formulas for the large periodic and antiperiodic eigenvalues and illustrate these formulas for the Kronig-Penney model. Then we give estimates for the small periodic and antiperiodic eigenvalues and for the length of the first gaps in the case of the Kronig-Penney model. Moreover, we give error estimations and present a numerical example. |
| title | On Explicit Estimations for the Bloch Eigenvalues of the One-dimensional Schrödinger Operator and the Kronig-Penney Model |
| topic | Spectral Theory Mathematical Physics 34L20, 47E05 |
| url | https://arxiv.org/abs/2501.10225 |