# FAST TRACK COMMUNICATION: An infinite family of solvable and integrable quantum systems on a plane

@article{Tremblay2009FASTTC, title={FAST TRACK COMMUNICATION: An infinite family of solvable and integrable quantum systems on a plane}, author={Fr{\'e}d{\'e}ric Tremblay and Alexander V. Turbiner and Pavel Winternitz}, journal={Journal of Physics A}, year={2009} }

An infinite family of exactly solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular cases of this family. The underlying algebraic structure of the new potentials is revealed as well as its hidden algebra. We conjecture that all members of the family are also superintegrable and demonstrate this for the first few cases. A quasi-exactly… Expand

#### 111 Citations

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