Finite-Gap Potentials and Integrable Geodesic Equations on a 2-Surface

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2024年12月1日

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S. V. Agapov,
A. E. Mironov

摘要

Abstract

We show that the one-dimensional Schrödinger equation can be viewed as the geodesic equation of a certain metric on a \(2\) -surface. In the case of the Schrödinger equation with a finite-gap potential, the metric and geodesics are explicitly found in terms of the Baker–Akhiezer function.