Superintegrability with third order invariants in quantum and classical mechanics

Details Superintegrability with third order invariants in quantum and classical mechanics Superintegrability with third order invariants in quantum and classical mechanics

2002-06-27

arxiv.org/abs/math-ph/0206046v1

J. Math. Phys. 43 (2002), no. 12, 5902--5912.

Physics

Mathematical Physics

15 pages

Scientific paper

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.

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