Finite-gap potentials and integrable geodesic equations on a 2-surface
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913661146103808 |
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| author | Agapov, S. V. Mironov, A. E. |
| author_facet | Agapov, S. V. Mironov, A. E. |
| contents | In this paper we show that the one-dimensional Schrödinger equation can be viewed as the geodesic equation of a certain metric on a 2-surface. In case of the Schrödinger equation with a finite-gap potential, the metric and geodesics are explicitly found in terms of the Baker--Akhiezer function |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12721 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite-gap potentials and integrable geodesic equations on a 2-surface Agapov, S. V. Mironov, A. E. Dynamical Systems Algebraic Geometry Differential Geometry 37J35, 34L05, 53D25, 14H70, 70H06 In this paper we show that the one-dimensional Schrödinger equation can be viewed as the geodesic equation of a certain metric on a 2-surface. In case of the Schrödinger equation with a finite-gap potential, the metric and geodesics are explicitly found in terms of the Baker--Akhiezer function |
| title | Finite-gap potentials and integrable geodesic equations on a 2-surface |
| topic | Dynamical Systems Algebraic Geometry Differential Geometry 37J35, 34L05, 53D25, 14H70, 70H06 |
| url | https://arxiv.org/abs/2501.12721 |