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Abstract: A complete classification is presented of quantum and classicalsuperintegrable systems in $E 2$ that allow the separation of variables inpolar coordinates and admit an additional integral of motion of order three inthe momentum. New quantum superintegrable systems are discovered for which thepotential is expressed in terms of the sixth Painlev\-e transcendent or interms of the Weierstrass elliptic function.



Author: Frederick Tremblay, Pavel Winternitz

Source: https://arxiv.org/







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