Hamiltonians separable in cartesian coordinates and third-order integrals of motion

Details Hamiltonians separable in cartesian coordinates and third-order integrals of motion Hamiltonians separable in cartesian coordinates and third-order integrals of motion

2003-02-11

arxiv.org/abs/math-ph/0302028v2

Journal of Mathematical Physics -- March 2004 -- Volume 45, Issue 3, pp. 1003-1019

Physics

Mathematical Physics

19 pages, Will be published in J. Math. Phys

Scientific paper

10.1063/1.1633352

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 mechanics. Many of these superintegrable systems are new, and it is seen that there exists a relation between quantum superintegrable potentials, invariant solutions of the Korteweg-De Vries equation and the Painlev\'e transcendents.

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