Browsing by Subject "quadratic algebras"
Now showing items 1-9 of 9
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Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras
(Institute of Mathematics of NAS of Ukraine, 2017)Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical ... -
Contractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials
(2013)We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-Inönü method ... -
Extended Kepler–Coulomb quantum superintegrable systems in three dimensions
(Institute of Physics, 2013)The quantum Kepler-Coulomb system in three dimensions is well known to be second order superintegrable, with a symmetry algebra that closes polynomially under commutators. This polynomial closure is also typical for second ... -
Laplace-type equations as conformal superintegrable systems
(Elsevier, 2010)We lay out the foundations of the theory of second order conformal superintegrable systems. Such systems are essentially Laplace equations on a manifold with an added potential: (Δn+V(x))Ψ=0. Distinct families of second ... -
Models for quadratic algebras associated with second order superintegrable systems in 2D
(SIGMA, 2008-01)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. We study the finite and infinite ... -
A recurrence relation approach to higher order quantum superintegrability
(2011)We develop our method to prove quantum superintegrability of an integrable 2D system, based on recurrence relations obeyed by the eigenfunctions of the system with respect to separable coordinates. We show that the method ... -
Structure theory for second order 2D superintegrable systems with 1-parameter potentials
(2009)The structure theory for the quadratic algebra generated by first and second order constants of the motion for 2D second order superintegrable systems with nondegenerate (3-parameter) and or 2-parameter potentials is well ... -
Tools for verifying classical and quantum superintegrability
(Kiev, 2010)Recently many new classes of integrable systems in n dimensions occurring in classical and quantum mechanics have been shown to admit a functionally independent set of 2n−1 symmetries polynomial in the canonical momenta, ... -
Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere
(2011)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 ...
