Schrödinger equations on elliptic curves: symmetries, solutions and eigenvalue problem

Schrödinger equations on elliptic curves: symmetries, solutions and eigenvalue problem

In this paper, we study Schrödinger equations on elliptic curves called generalized Lamé equations. We suggest a method of finding integrable potentials for Schrödinger type equations. We apply this method to the Lamé equations and provide a sequence of integrable potentials for which the eigenvalue...

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Veröffentlicht in:Analysis and mathematical physics 2020-09, Vol.10 (3), Article 34
Hauptverfasser: Lychagin, Valentin, Roop, Mikhail
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Curves
Eigenvalues
Elliptic functions
Lame functions
Mathematical analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Schrodinger equation
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Zusammenfassung:In this paper, we study Schrödinger equations on elliptic curves called generalized Lamé equations. We suggest a method of finding integrable potentials for Schrödinger type equations. We apply this method to the Lamé equations and provide a sequence of integrable potentials for which the eigenvalue problem is solved explicitly.
ISSN:1664-2368
1664-235X
DOI:10.1007/s13324-020-00377-0