Classification of quantum superintegrable systems with quadratic integrals on two dimensional manifolds

@inproceedings{Tanoudes2006ClassificationOQ,
  title={Classification of quantum superintegrable systems with quadratic integrals on two dimensional manifolds},
  author={C. Daskaloyannis And Y. Tanoudes},
  year={2006}
}
There are two classes of quantum integrable systems on a manifold with quadratic integrals, the Liouville and the Lie integrable systems as it happens in the classical case. The quantum Liouville quadratic integrable systems are defined on a Liouville manifold and the Schr¨odinger equation can be solved by separation of variables in one coordinate system. The Lie integrable systems are defined on a Lie manifold and are not generally separable ones but the can be solved. Therefore there are… 

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