On the superintegrability of TTW model

The superintegrability of so-called Tremblay–Turbiner–Winternitz (TTW) model has been conjectured on the basis of the fact that all its trajectories are closed. This conjecture has been proven using the method based on solving the partial differential equations for two functions having the same Poisson bracket with the Hamiltonian. In the present short Letter we show that superintegrability of TTW model can be established by using well-known elegant techniques of analytical mechanics. Moreover, the resulting expression (after an appropriate ordering) can be generalized to the quantum-mechanical case.