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

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

URL: http://arxiv.org/abs/2309.16886v2
Date: Mon, 23 Oct 2023 02:16:17 GMT
Title: Two-body Coulomb problem and hidden $g^{(2)}$ algebra: superintegrability and cubic polynomial algebra
Authors: Alexander V. Turbiner and Adrian M. Escobar-Ruiz
Abstract summary: 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. The two integrals are integral of orders two and four, they are made from two components of the angular momentum and from the modified LaplaceRunge-Lenz vector.
Score: 55.2480439325792
License: http://creativecommons.org/licenses/by/4.0/
Abstract: 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 $U_{g^{(2)}}$.

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