Hamiltonians separable in cartesian coordinates and third-order integrals of motion
数学物理
2007-05-23 v2 动力系统
math.MP
摘要
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.
引用
@article{arxiv.math-ph/0302028,
title = {Hamiltonians separable in cartesian coordinates and third-order integrals of motion},
author = {Simon Gravel},
journal= {arXiv preprint arXiv:math-ph/0302028},
year = {2007}
}
备注
19 pages, Will be published in J. Math. Phys