A remark on the Tremblay-Turbiner-Winternitz potential

Abstract We verify, using a polar representation of the vector space of Killing tensors of valence two defined in the Euclidean plane, that the Tremblay-Turbiner-Winternitz (TTW) potential, an important integrable perturbation of the Smorodinsky-Winternitz potential, loses the property of multi-separability for all but two specific values of the arbitrary parameter k .