Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2013
• Main Authors: Kalnins, E.G., Miller Jr., W., Post, S.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2013
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149341
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials / E.G. Kalnins, W. Miller Jr., S. Post // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 40 назв. — англ.

We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-Inönü method of Lie algebra contractions to contractions of quadratic algebras and show that...