Two-body Coulomb problem and hidden $g^{(2)}$ algebra: superintegrability and cubic polynomial algebra

J.Phys.: Conference Series, 2667 (2023) 012075 It is shown that the two-body Coulomb problem in the Sturm representation leads to a new two-dimensional, exactly-solvable, superintegrable quantum system in curved space with a $g^{(2)}$ hidden algebra and a cubic polynomial algebra of integrals. The t...

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Bibliographic Details
Main Authors Turbiner, Alexander V, Escobar-Ruiz, Adrian M
Format Journal Article
LanguageEnglish
Published 28.09.2023
Subjects
Mathematics - Mathematical Physics
Physics - Mathematical Physics
Physics - Quantum Physics
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Summary:J.Phys.: Conference Series, 2667 (2023) 012075 It is shown that the two-body Coulomb problem in the Sturm representation leads to a new two-dimensional, exactly-solvable, superintegrable quantum system in curved space with a $g^{(2)}$ hidden algebra and a cubic polynomial algebra of integrals. The two integrals are of orders two and four, they are made from two components of the angular momentum and from the modified Laplace-Runge-Lenz vector, respectively. It is demonstrated that the cubic polynomial algebra is an infinite-dimensional subalgebra of the universal enveloping algebra $U_{g^{(2)}}$.
DOI:10.48550/arxiv.2309.16886