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math-ph2017★ 7 cited
Fifth-order superintergrable quantum system separating in Cartesian coordinates. Doubly exotic potentials
Ismail Abouamal, Pavel Winternitz
We consider a two dimensional quantum Hamiltonian separable in Cartesian coordinates and allowing a fifth-order integral of motion. We impose the superintegrablity condition and fi…
math-ph2017★ 27 cited
Fourth order superintegrable systems separating in Polar Coordinates. I. Exotic Potentials
Adrian M. Escobar-Ruiz, J. C. López Vieyra, P. Winternitz
We present all real quantum mechanical potentials in a two-dimensional Euclidean space that have the following properties: 1. They allow separation of variables of the Schrödinger…