Quantum superintegrable system with a novel chain structure of quadratic algebras

DOI10.1088/1751-8121/aac111zbMath1395.81110arXiv1801.05634OpenAlexW3098521301WikidataQ57999095 ScholiaQ57999095MaRDI QIDQ4578190

Ian Marquette, Yidong Liao, Yao-Zhong Zhang

Publication date: 8 August 2018

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.05634

zbMATH Keywords

Schrödinger equationquadratic algebrassuperintegrable systems

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Groups and algebras in quantum theory and relations with integrable systems (81R12) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Operator algebra methods applied to problems in quantum theory (81R15) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (11)

Universal chain structure of quadratic algebras for superintegrable systems with coalgebra symmetry ⋮ Embedding of the Racah algebra \(R(n)\) and superintegrability ⋮ Hidden symmetry algebra and construction of quadratic algebras of superintegrable systems ⋮ Extended Laplace-Runge-Lentz vectors, new family of superintegrable systems and quadratic algebras ⋮ Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras ⋮ Higher Order Quantum Superintegrability: A New “Painlevé Conjecture” ⋮ Quadratic algebras as commutants of algebraic Hamiltonians in the enveloping algebra of Schrödinger algebras ⋮ The general Racah algebra as the symmetry algebra of generic systems on pseudo-spheres ⋮ Polynomial algebras from su(3) and a quadratically superintegrable model on the two sphere ⋮ N-dimensional Smorodinsky–Winternitz model and related higher rank quadratic algebra SW(N) ⋮ Racah algebra R(n) from coalgebraic structures and chains of R(3) substructures

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