# Superintegrability and higher-order constants for classical and quantum systems

@article{Kalnins2011SuperintegrabilityAH, title={Superintegrability and higher-order constants for classical and quantum systems}, author={Ernie G. Kalnins and Willard Miller and George S. Pogosyan}, journal={Physics of Atomic Nuclei}, year={2011}, volume={74}, pages={914-918} }

We extend recent work by Tremblay, Turbiner, and Winternitz which analyzes an infinite family of solvable and integrable quantum systems in the plane, indexed by the positive parameter k. Key components of their analysis were to demonstrate that there are closed orbits in the corresponding classical system if k is rational, and for a number of examples there are generating quantum symmetries that are higher order differential operators than two. Indeed they conjectured that for a general class…

## 59 Citations

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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.…

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The family of Tremblay–Turbiner–Winternitz (TTW) Hamiltonians Hk on a plane, corresponding to any positive real value of k, is shown to admit another supersymmetric extension than that previously…

N = 2 supersymmetric extension of the Tremblay-Turbiner-Winternitz Hamiltonians on a plane

- Mathematics
- 2010

The family of Tremblay–Turbiner–Winternitz Hamiltonians Hk on a plane, corresponding to any positive real value of k, is shown to admit an supersymmetric extension of the same kind as that introduced…

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Quantum versions of the hydrogen atom and the harmonic oscillator are studied on non Euclidean spaces of dimension N. integrals, of arbitrary order, are constructed via a multi-dimensional version of…

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We introduce a new family of Hamiltonians with a deformed Kepler–Coulomb potential dependent on an indexing parameter k. We show that this family is superintegrable for all rational k and compute the…

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