Geodesic
Superintegrable Systems with Third-Order Integrals in Classical and Quantum Mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 1, pp. 97-107 Cet article a éte moissonné depuis la source Math-Net.Ru

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We review systems in $E(2)$ that are separable in Cartesian coordinates and admit a third-order integral both in quantum mechanics and in classical mechanics. Differences and similarities between those two cases are illustrated by numerous examples. Many of these superintegrable systems are new, and a relation is seen between superintegrable potentials and Painlevé transcendents.
Keywords: integrals of motion, superintegrability, separation of variables. 
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S. Gravel. Superintegrable Systems with Third-Order Integrals in Classical and Quantum Mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 1, pp. 97-107. http://geodesic.mathdoc.fr/item/TMF_2003_137_1_a10/

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