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There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries.
Friš J., Mandrosov V., Smorodinsky Ya.A., Uhlír M., Winternitz P., On higher symmetries in quantum mechanics,
1965
Earlier work this paper cites.
Calogero F., Solution to the one-dimensional
1971
Earlier work this paper cites.
Koenigs G., Sur les géodésiques a intégrales quadratiques, A note appearing in “Lecons sur la théorie générale des surfaces”, G. Darboux, Vol. 4, Chelsea Publishing, 1972, 368–404
1972
Earlier work this paper cites.
Arnold V.I., Mathematical methods of classical mechanics (translated by K. Vogtmann and A. Weinstein)
1978
Earlier work this paper cites.
Wojciechowski S., Superintegrability of the Calogero–Moser system,
1983
Earlier work this paper cites.
Kalnins E.G., Separation of variables for Riemannian spaces of constant curvature,
1986
Earlier work this paper cites.
Evans N.W., Super-integrability of the Winternitz system,
1990
Earlier work this paper cites.
Evans N.W., Superintegrability in classical mechanics,
1991
Earlier work this paper cites.
Zhedanov A.S., “Hidden symmetry” of Askey–Wilson polynomials,
1991
Earlier work this paper cites.
Granovskii Ya.I., Zhedanov A.S., Lutsenko I.M., Quadratic algebras and dynamics in curved spaces. I. Oscillator,
1992
Earlier work this paper cites.
Granovskii Ya.I., Zhedanov A.S., Lutsenko I.M., Quadratic algebras and dynamics in curved spaces. II. The Kepler problem,
1992
Earlier work this paper cites.
Bonatos D., Daskaloyannis C., Kokkotas K., Deformed oscillator algebras for two-dimensional quantum superintegrable systems,
1994
Earlier work this paper cites.
Quesne C., Generalized deformed parafermions, nonlinear deformations of so(3) and exactly solvable potentials,
1994
Earlier work this paper cites.
Letourneau P., Vinet L., Superintegrable systems: polynomial algebras and quasi-exactly solvable Hamiltonians,
1995
Earlier work this paper cites.
Rañada M.F., Superintegrable
1997
Earlier work this paper cites.
Andrews G.E., Askey R., Roy R., Special functions,
1999
Earlier work this paper cites.
Kalnins E.G., Miller W. Jr., Pogosyan G.S., Completeness of multiseparable superintegrability in
2000
Cited alongside, same era.
Kalnins E.G., Miller W. Jr., Pogosyan G.S., Completeness of multiseparable superintegrability on the complex 2-sphere,
2000
Cited alongside, same era.
Daskaloyannis C., Quadratic Poisson algebras of two-dimensional classical superintegrable systems and quadratic associative algebras of quantum superintegrable systems,
2001
Cited alongside, same era.
Kalnins E.G., Kress J.M., Miller W. Jr., Pogosyan G.S., Completeness of superintegrability in two-dimensional constant curvature spaces,
2001
Cited alongside, same era.
Tempesta P., Turbiner A.V., Winternitz P., Exact solvability of superintegrable systems,
2001
Cited alongside, same era.
Horwood J.T., McLenaghan R.G., Smirnov R.G., Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space,
2005
Later among the works it cites.
Kalnins E.G., Kress J.M., Miller W. Jr., Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Stäckel transform and 3D classification theory,
2006
Later among the works it cites.
Kalnins E.G., Kress J.M., Miller W. Jr., Second order superintegrable systems in conformally flat spaces. V. 2D and 3D quantum systems,
2006
Later among the works it cites.
Kalnins E.G., Miller W. Jr., Pogosyan G.S., Exact and quasi-exact solvability of second order superintegrable systems. I. Euclidean space preliminaries,
2006
Later among the works it cites.
Daskaloyannis C., Ypsilantis K., Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensional manifold,
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Kalnins E.G., Miller W. Jr., Williams G.C., Pogosyan G.S., On superintegrable symmetry-breaking potentials in
2002
Cited alongside, same era.
Gravel S., Winternitz P., Superintegrability with third-order integrals in quantum and classical mechanics,
2002
Cited alongside, same era.
Kalnins E.G., Kress J.M., Winternitz P., Superintegrability in a two-dimensional space of non-constant curvature,
2002
Cited alongside, same era.
Ballesteros A., Herranz F., Santander M., Sanz-Gil T., Maximal superintegrability on
2003
Cited alongside, same era.
Kalnins E.G., Kress J.M., Miller W. Jr., Winternitz P., Superintegrable systems in Darboux spaces,
2003
Cited alongside, same era.
Tempesta P., Winternitz P., Miller W., Pogosyan G. (Editors), Superintegrability in classical and quantum systems,
2004
Cited alongside, same era.
Gravel S., Hamilton separable in Cartesian coordinates and third-order integrals of motion,
2004
Cited alongside, same era.
2006
Later among the works it cites.
Kalnins E.G., Kress J.M., Miller W. Jr., Nondegenerate 2D complex Euclidean superintegrable systems and algebraic varieties,
2007
Later among the works it cites.
Kalnins E.G., Kress J.M., Miller W. Jr., Fine structure for 3D second order superintegrable systems: 3-parameter potentials,
2007
Later among the works it cites.
2007
Later among the works it cites.
2007
Later among the works it cites.
Daskaloyannis C., Tanoudis Y., Quantum superintegrable systems with quadratic integrals on a two dimensional manifold,
2007
Later among the works it cites.
Kalnins E.G., Miller W. Jr., Post S., Wilson polynomials and the generic superintegrable system on the 2-sphere,
2007
Later among the works it cites.
Ballesteros A., Herranz F.J., Universal integrals for superintegrable systems on
2007
Later among the works it cites.
Fordy A.P., Quantum super-integrable systems as exactly solvable models,
2007
Later among the works it cites.
Kalnins E.G., Miller W. Jr., Pogosyan G.S., Exact and quasi-exact solvability of second order superintegrable quantum systems. II. Connection with separation of variables,
2007
Later among the works it cites.
Kress J.M., Equivalence of superintegrable systems in two dimensions,
2007
Later among the works it cites.