77 citations · 173 across the 4 of their papers we have counts for
4 papers
Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics I:Rational function potentials
Ian Marquette
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the mos…
Superintegrable Systems with a Third Order Integrals of Motion
Ian Marquette, Pavel Winternitz
Two-dimensional superintegrable systems with one third order and one lower order integral of motion are reviewed. The fact that Hamiltonian systems with higher order integrals of m…
Polynomial Associative Algebras for Quantum Superintegrable Systems with a Third Order Integral of Motion
Ian Marquette
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the mos…
Polynomial Poisson Algebras for Classical Superintegrable Systems with a Third Order Integral of Motion
I. Marquette, P. Winternitz
We present polynomial Poisson algebras for the 8 classical potentials in two-dimensional Euclidian space that separate in cartesian coordinates and allow a third order integral of…