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We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators).
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Kalnins E.G., Miller W. Jr., Tratnik M.V., Families of orthogonal and biorthogonal polynomials on the
1991
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Kalnins E.G., Kress J.M., Pogosyan G.S., Miller W. Jr., Completeness of superintegrability in two-dimensional constant-curvature spaces,
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Curtright T.L., Zachos C.K., Deformation quantization of superintegrable systems and Nambu mechanics,
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Cordani B., The Kepler problem. Group theoretical aspects, regularization and quantization, with application to the study of perturbations,
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Tempesta P., Winternitz P., Harnad J., Miller W., Pogosyan G., Rodriguez M. (Editors), Superintegrability in classical and quantum systems (September 16–21, 2002 Montreal, Canada),
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Zachos C.K., Curtright T.L., Branes, quantum Nambu brackets and the hydrogen atom,
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Curtis H.D., Orbital mechanics for engineering students, Aerospace Enineering Series, Elsevier, Amsterdam, 2005
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Kalnins E.G., Kress J.M., Miller W. Jr., Second order superintegrable systems in conformally flat spaces. II. The classical two-dimensional Stäckel transform,
2005
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Kalnins E.G., Kress J.M., Miller W. Jr., Second-order superintegrable systems in conformally flat spaces. I. Two-dimensional classical structure theory,
2005
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Kalnins E.G., Kress J.M., Miller W. Jr., Second order superintegrable systems in conformally flat spaces. III. Three-dimensional classical structure,
2005
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Gasper G., Rahman M., Some systems of multivariable orthogonal Askey–Wilson polynomials, in Theory and Applications of Special Functions,
2005
Cited alongside, same era.
Kalnins E.G., Kress J.M., Miller W. Jr., Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems,
2006
Cited alongside, same era.
Daskaloyannis C., Ypsilantis K., Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensional manifold,
2006
Cited alongside, same era.
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
Cited alongside, same era.
Kalnins E.G., Miller W. Jr., Post S., Models for the 3D singular isotropic oscillator quadratic algebra,
2009
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2010
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2010
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Post S., Winternitz P., An infinite family of superintegrable deformations of the Coulomb potential,
2010
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Kalnins E.G., Miller W. Jr., Post S., Coupling constant metamorphosis and
2010
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2007
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Kalnins E.G., Miller W. Jr., Post S., Wilson polynomials and the generic superintegrable system on the 2-sphere,
2007
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Kalnins E.G., Kress J.M., Miller W. Jr., Pogosyan G., Nondegenerate superintegrable systems in
2007
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Eastwood M., Miller W. (Editors), Symmetries and overdetermined systems of partial differential equations (July 17 – August 4, 2006, Minneapolis, MN),
2008
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2008
Cited alongside, same era.
Chanu C., Degiovanni L., Rastelli G., Superintegrable three-body systems on the line,
2008
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Verrier P.E., Evans N.W., A new superintegrable Hamiltonian,
2008
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2009
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Marquette I., Superintegrability and higher order polynomial algebras,
2010
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Geronimo J.S., Iliev P., Bispectrality of multivariable Racah–Wilson polynomials,
2010
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2011
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Tratnik M.V., Some multivariable orthogonal polynomials of the Askey tableau-continuous families,
2073
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