# 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}
}
• C. Quesne
• Published 23 November 2009
• Mathematics
• arXiv: Mathematical Physics
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…
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