# Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd $k$

@article{Quesne2009SuperintegrabilityOT, title={Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd \$k\$}, author={C Quesne}, journal={arXiv: Mathematical Physics}, year={2009} }

In a recent FTC by Tremblay {\sl et al} (2009 {\sl J. Phys. A: Math. Theor.} {\bf 42} 205206), it has been conjectured that for any integer value of $k$, some novel exactly solvable and integrable quantum Hamiltonian $H_k$ on a plane is superintegrable and that the additional integral of motion is a $2k$th-order differential operator $Y_{2k}$. Here we demonstrate the conjecture for the infinite family of Hamiltonians $H_k$ with odd $k \ge 3$, whose first member corresponds to the three-body…

## 54 Citations

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