N-dimensional Smorodinsky–Winternitz model and related higher rank quadratic algebra SW(N)

@article{Correa2021NdimensionalSM,
  title={N-dimensional Smorodinsky–Winternitz model and related higher rank quadratic algebra SW(N)},
  author={Francisco Correa and Md Fazlul Hoque and Ian Marquette and Yao-Z Zhang},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2021},
  volume={54}
}
The N-dimensional Smorodinsky–Winternitz system is a maximally superintegrable and exactly solvable model, being subject of study from different approaches. The model has been demonstrated to be multiseparable with wavefunctions given by Laguerre and Jacobi polynomials. In this paper we present the complete symmetry algebra SW(N) of the system, which it is a higher-rank quadratic one containing the recently discovered Racah algebra R(N) as subalgebra. The substructures of distinct quadratic Q(3… Expand

References

SHOWING 1-10 OF 47 REFERENCES
Revisiting the symmetries of the quantum smorodinsky-winternitz system in D dimensions
The D-dimensional Smorodinsky{Winternitz system, proposed some years ago by Evans, is re-examined from an algebraic viewpoint. It is shown to possess a potential algebra, as well as a dynamicalExpand
Lie-algebraic description of the quantum superintegrable Smorodinsky?Winternitz system in n dimensions
We apply the potential group method to a family of n-dimensional quantum Smorodinsky?Winternitz systems. The Hamiltonians of the systems are associated with first-order Casimir operators of theExpand
A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) ⨁ so(n) ⨁ so(N-n)
We introduce a new family of N dimensional quantum superintegrable models consisting of double singular oscillators of type (n, N-n). The special cases (2,2) and (4,4) have previously been identifiedExpand
Nondegenerate 2D complex Euclidean superintegrable systems and algebraic varieties
A classical (or quantum) superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n − 1 functionally independent constants of the motion polynomial in theExpand
Group theory of the Smorodinsky-Winternitz system
The three degrees of freedom Smorodinsky–Winternitz system is a degenerate or super‐integrable Hamiltonian that possesses five functionally independent globally defined and single‐valued integrals ofExpand
Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials
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 extendExpand
Quadratic algebra structure and spectrum of a new superintegrable system in N-dimension
We introduce a new superintegrable Kepler–Coulomb system with non-central terms in N-dimensional Euclidean space. We show this system is multiseparable and allows separation of variables inExpand
Toward a classification of semidegenerate 3D superintegrable systems
Superintegrable systems of 2nd order in 3 dimensions with exactly 3-parameter potentials are intriguing objects. Next to the nondegenerate 4-parameter potential systems they admit the maximum numberExpand
Quantum superintegrability and exact solvability in n dimensions
A family of maximally superintegrable systems containing the Coulomb atom as a special case is constructed in n-dimensional Euclidean space. Two different sets of n commuting second-order operatorsExpand
Quantum superintegrable system with a novel chain structure of quadratic algebras
We analyse the n-dimensional superintegrable Kepler-Coulomb system with non-central terms. We find a novel underlying chain structure of quadratic algebras formed by the integrals of motion. WeExpand
...
1
2
3
4
5
...