Exact solvability of superintegrable systems
Copyright policy )Exact solvability of superintegrable systems
It is shown that all four superintegrable quantum systems on the Euclidean plane possess the same underlying hidden algebra sl(3). The gauge-rotated Hamiltonians, as well as their integrals of motion, once rewritten in appropriate coordinates, preserve a flag of polynomials. This flag corresponds to highest-weight finite-dimensional representations of the sl(3)-algebra, realized by first-order differential operators.
- Laboratoire de Physique Théorique France
- University of Montreal Canada
- University of Paris-Saclay France
High Energy Physics - Theory, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Groups and algebras in quantum theory and relations with integrable systems, Mathematical Physics (math-ph), Exactly and quasi-solvable systems arising in quantum theory, Finite-dimensional groups and algebras motivated by physics and their representations, Euclidean plane, High Energy Physics - Theory (hep-th), hidden algebra \(sl(3)\), Exactly Solvable and Integrable Systems (nlin.SI), integrals of motion, Mathematical Physics, highest-weight finite-dimensional representations
High Energy Physics - Theory, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Groups and algebras in quantum theory and relations with integrable systems, Mathematical Physics (math-ph), Exactly and quasi-solvable systems arising in quantum theory, Finite-dimensional groups and algebras motivated by physics and their representations, Euclidean plane, High Energy Physics - Theory (hep-th), hidden algebra \(sl(3)\), Exactly Solvable and Integrable Systems (nlin.SI), integrals of motion, Mathematical Physics, highest-weight finite-dimensional representations
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