Finite-gap potentials and integrable geodesic equations on a 2-surface
Dynamical Systems
2025-01-23 v1 Algebraic Geometry
Differential Geometry
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
Cite
@article{arxiv.2501.12721,
title = {Finite-gap potentials and integrable geodesic equations on a 2-surface},
author = {S. V. Agapov and A. E. Mironov},
journal= {arXiv preprint arXiv:2501.12721},
year = {2025}
}