Quantum super-integrable systems as exactly solvable models

DOI10.3842/SIGMA.2007.025zbMath1136.81027arXivmath-ph/0702048MaRDI QIDQ2473421

Allan P. Fordy

Publication date: 27 February 2008

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0702048

zbMATH Keywords

Laplace-Beltrami operatorexact solvabilityquantum integrabilitysuper-integrability

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Exactly and quasi-solvable systems arising in quantum theory (81U15) Groups and algebras in quantum theory and relations with integrable systems (81R12) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)

Related Items (14)

Bôcher contractions of conformally superintegrable Laplace equations ⋮ Integrable and superintegrable extensions of the rational Calogero–Moser model in three dimensions ⋮ Universal chain structure of quadratic algebras for superintegrable systems with coalgebra symmetry ⋮ A Kaluza-Klein reduction of super-integrable systems ⋮ Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential ⋮ A note on some superintegrable Hamiltonian systems ⋮ Hamiltonian and super-Hamiltonian systems of a hierarchy of soliton equations ⋮ Recursive procedures for Krall-Sheffer operators ⋮ Poisson algebras and 3D superintegrable Hamiltonian systems ⋮ Bôcher and abstract contractions of 2nd order quadratic algebras ⋮ Hamiltonian and super-Hamiltonian extensions related to Broer-Kaup-Kupershmidt system ⋮ First integrals from conformal symmetries: Darboux-Koenigs metrics and beyond ⋮ The role of commuting operators in quantum superintegrable systems ⋮ New infinite families of Nth-order superintegrable systems separating in Cartesian coordinates

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