极坐标系下的三阶超可积系统
Third order superintegrable systems separating in polar coordinates
摘要：
在$E_2$中给出了量子和经典超可积系统的一个完整分类，它允许在极坐标中分离变量，并允许在动量中附加三阶运动积分。发现了新的量子超可积系统，其势可用第六Painlevé超越函数或Weierstrass椭圆函数表示。
英文摘要：
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 Painlevé transcendent or in terms of the Weierstrass elliptic function.
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