|
Finite-gap potentials and integrable geodesic equations on a 2-surface
S. V. Agapovab, A. E. Mironovab
a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Abstract:
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.
Keywords:
Schrödinger equation, finite-gap potential, Baker—Akhiezer function, metrisability, geodesics, integrability
Received: June 6, 2024
Revised: July 1, 2024
Accepted: August 13, 2024
Linking options:
https://www.mathnet.ru/eng/tm4435
|
|
Contact us: