Superintegrability with third order invariants in quantum and classical mechanics
Mathematical Physics
2015-06-26 v1 math.MP
Abstract
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 integrals, and all their integrals. Quantum superintegrable systems are found that have no classical analog, i.e. the potentials are proportional to \hbar^2, so their classical limit is free motion.
Cite
@article{arxiv.math-ph/0206046,
title = {Superintegrability with third order invariants in quantum and classical mechanics},
author = {Simon Gravel and Pavel Winternitz},
journal= {arXiv preprint arXiv:math-ph/0206046},
year = {2015}
}
Comments
15 pages