2017/03/28 by Ian Marquette, Masoumeh Sajedi, Pavel Winternitz · 2 citations
Physics and Astronomy · Mathematics · #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8121/aa7a67
published as J.Phys.A Theor. and Math 50 315201 (2017) · 36 pages
arxiv created 2017/03/28 · arxiv updated 2018/01/24
A study is presented of two-dimensional superintegrable systems separating in Cartesian coordinates and allowing an integral of motion that is a fourth order polynomial in the momenta. All quantum mechanical potentials that do not satisfy any linear differential equation are found. They do however satisfy nonlinear ODEs. We show that these equations always have the Painlevé property and integrate them in terms of known Painlevé transcendents or elliptic functions.