# Classical and Quantum Superintegrability of Stäckel Systems

@article{Baszak2017ClassicalAQ, title={Classical and Quantum Superintegrability of St{\"a}ckel Systems}, author={Maciej Błaszak and Krzysztof Marciniak}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2017}, volume={13}, pages={008} }

In this paper we discuss maximal superintegrability of both classical and quantum Stackel systems. We prove a sufficient condition for a flat or constant curvature Stackel system to be maximally su ...

## 5 Citations

### Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics

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A non-degenerate second-order maximally conformally superintegrable system in dimension 2 naturally gives rise to a quadric with position dependent coefficients. It is shown how the system's Stackel…

### Non-Homogeneous Hydrodynamic Systems and Quasi-Stackel Hamiltonians

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In this paper we present a novel construction of non-homogeneous hydrodynamic equations from what we call quasi-Stackel systems, that is non-commutatively integrable systems constructed from approp…

### Stäckel transform of Lax equations

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- 2020

We construct a map between Lax equations for pairs of Liouville integrable Hamiltonian systems related by a multiparameter Stäckel transform. Using this map, we construct Lax representation for a…

### Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion

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It is natural to investigate if the quantization of integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of…

### Algebraic Conditions for Conformal Superintegrability in Arbitrary Dimension

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- 2020

Second-order conformally superintegrable systems generalise second-order (properly) superintegrable systems. They have been classified, essentially, in dimensions two and (partially) three only. For…

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