Browsing by Author "Post, Sarah"
Now showing items 1-5 of 7
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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 ... -
Coupling constant metamorphosis and Nth-order symmetries in classical and quantum mechanics
(IOP Publishing, 2010)We review the fundamentals of coupling constant metamorphosis (CCM) and the Stäckel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on different manifolds. In ... -
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 ... -
Models for the 3D Singular Isotropic Oscillator Quadratic Algebra
(MAIK NAUKA/INTERPERIODICA/SPRINGER, 2010-02-01)We give the first explicit construction of the quadratic algebra for a 3D quantum superintegrable system with nondegenerate (4-parameter) potential together with realizations of irreducible representations of the quadratic ...
