3 problems

Exact-solvability conjecture. Exactly solvability should hold quite widely for super-integrable systems.

Let $H_1$ and $I_2$ be the first integrals in case 2 of Theorem, let $d=-(2p-1)/2$ with $p\in\mathbb{N}$, and let $\widetilde{H}_{3,p}$ denote the additional first integral. Polyno…

Super-integrability conjecture. The system is super-integrable for arbitrary integer $n$. For small integer values of $n$, the corresponding quantum system is known to be super-int…