Generalized Hermite Polynomials and Monodromy-Free Schrödinger Operators

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Author: Novokshenov, V.Yu.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209851
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Generalized Hermite Polynomials and Monodromy-Free Schrödinger Operators / V.Yu. Novokshenov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 28 назв. — англ.

The paper gives a review of recent progress in the classification of monodromy-free Schrödinger operators with rational potentials. We concentrate on a class of potentials constituted by generalized Hermite polynomials. These polynomials, defined as Wronskians of classic Hermite polynomials, appear...