Third order superintegrable systems separating in polar coordinates

Details Third order superintegrable systems separating in polar coordinates Third order superintegrable systems separating in polar coordinates

2010-02-09

arxiv.org/abs/1002.1989v1

Physics

Mathematical Physics

Scientific paper

A complete classification is presented of quantum and classical superintegrable systems in $E_2$ that allow the separation of variables in polar coordinates and admit an additional integral of motion of order three in the momentum. New quantum superintegrable systems are discovered for which the potential is expressed in terms of the sixth Painlev\'e transcendent or in terms of the Weierstrass elliptic function.

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