Classical and Quantum Superintegrability of Stäckel Systems

Maciej Błaszak ; Krzysztof Marciniak

Symmetry, integrability and geometry: methods and applications, Tome 13 (2017)

Résumé

In this paper we discuss maximal superintegrability of both classical and quantum Stäckel systems. We prove a sufficient condition for a flat or constant curvature Stäckel system to be maximally superintegrable. Further, we prove a sufficient condition for a Stäckel transform to preserve maximal superintegrability and we apply this condition to our class of Stäckel systems, which yields new maximally superintegrable systems as conformal deformations of the original systems. Further, we demonstrate how to perform the procedure of minimal quantization to considered systems in order to produce quantum superintegrable and quantum separable systems.

Détail

Keywords: Hamiltonian systems; classical and quantum superintegrable systems; Stäckel systems; Hamilton–Jacobi theory; Stäckel transform.

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