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arXiv · 2501.12721

Finite-gap potentials and integrable geodesic equations on a 2-surface

S. V. Agapov·A. E. Mironov
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Abstract

In this paper we show that the one-dimensional Schr\"odinger equation can be viewed as the geodesic equation of a certain metric on a 2-surface. In case of the Schr\"odinger equation with a finite-gap potential, the metric and geodesics are explicitly found in terms of the Baker--Akhiezer function

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S. V. Agapov, A. E. Mironov. 2025-01-22. Finite-gap potentials and integrable geodesic equations on a 2-surface. https://doi.org/10.4213/tm4435

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