376 citations · 792 across the 13 of their papers we have counts for
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math-ph2003★ 4 cited
Superintegrability, isochronicity, and quantum harmonic behavior
Simon Gravel
We discuss the properties of superintegrable Hamiltonian systems, in particular those that admit separation of variables in cartesian coordinates. We show that the superintegrabili…
math-ph2003★ 89 cited
Hamiltonians separable in cartesian coordinates and third-order integrals of motion
Simon Gravel
We present in this article all Hamiltonian systems in E(2) that are separable in cartesian coordinates and that admit a third-order integral, both in quantum and in classical mecha…
math-ph2002★ 131 cited
Superintegrability with third order invariants in quantum and classical mechanics
Simon Gravel, Pavel Winternitz
We consider here the coexistence of first- and third-order integrals of motion in two dimensional classical and quantum mechanics. We find explicitly all potentials that admit such…