scholarly journals Family ofN-dimensional superintegrable systems and quadratic algebra structures

2016 ◽  
Vol 670 ◽  
pp. 012024 ◽  
Author(s):  
Md Fazlul Hoque ◽  
Ian Marquette ◽  
Yao-Zhong Zhang
Keyword(s):  
Quadratic Algebra ◽  
Superintegrable Systems

scholarly journals Quadratic algebra contractions and second-order superintegrable systems

2014 ◽  
Vol 12 (05) ◽  
pp. 583-612 ◽  
Author(s):  
Ernest G. Kalnins ◽  
W. Miller
Keyword(s):  
Constant Curvature ◽  
Two Dimensions ◽  
Second Order ◽  
Quadratic Algebra ◽  
Quadratic Algebras ◽  
Physical Systems ◽  
Special Cases ◽  
Superintegrable Systems ◽  
Wilson Polynomials ◽  
Symmetry Algebras

Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of second-order superintegrable systems in two dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. For constant curvature spaces, we show that the free quadratic algebras generated by the first- and second-order elements in the enveloping algebras of their Euclidean and orthogonal symmetry algebras correspond one-to-one with the possible superintegrable systems with potential defined on these spaces. We describe a contraction theory for quadratic algebras and show that for constant curvature superintegrable systems, ordinary Lie algebra contractions induce contractions of the quadratic algebras of the superintegrable systems that correspond to geometrical pointwise limits of the physical systems. One consequence is that by contracting function space realizations of representations of the generic superintegrable quantum system on the 2-sphere (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials.

scholarly journals Klein-Gordon Equation with Superintegrable Systems: Kepler-Coulomb, Harmonic Oscillator, and Hyperboloid

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
V. Mohammadi ◽  
S. Aghaei ◽  
A. Chenaghlou
Keyword(s):  
Harmonic Oscillator ◽  
Coulomb Potential ◽  
Gordon Equation ◽  
Spin Symmetry ◽  
Quadratic Algebra ◽  
Relativistic Energy ◽  
Algebra Approach ◽  
Superintegrable Systems ◽  
Klein Gordon ◽  
Klein Gordon Equation

We study the two-dimensional Klein-Gordon equation with spin symmetry in the presence of the superintegrable potentials. On Euclidean space, theSO(3)group generators of the Schrödinger-like equation with the Kepler-Coulomb potential are represented. In addition, by Levi-Civita transformation, the Schrödinger-like equation with harmonic oscillator which is dual to the Kepler-Coulomb potential and theSU(2)group generators of associated system are studied. Also, we construct the quadratic algebra of the hyperboloid superintegrable system. Then, we obtain the corresponding Casimir operators and the structure functions and the relativistic energy spectra of the corresponding quasi-Hamiltonians by using the quadratic algebra approach.

Superintegrable Systems with Arbitrary Spin

2013 ◽  
Vol 58 (11) ◽  
pp. 1046-1054 ◽  
Author(s):  
A.G. Nikitin ◽  
Keyword(s):  
Arbitrary Spin ◽  
Superintegrable Systems

Nambu-Poisson dynamics of superintegrable systems

2007 ◽  
Vol 70 (3) ◽  
pp. 567-571 ◽  
Author(s):  
N. Makhaldiani
Keyword(s):  
Superintegrable Systems
Sign in / Sign up

Export Citation Format

Share Document