Fifth-order superintegrable quantum systems separating in Cartesian coordinates: Doubly exotic potentials
3rd International Conference on Applied Physics
August 23-24, 2018 | London, UK
University of Toronto, Canada
Posters & Accepted Abstracts : J Appl Math Stat App
We consider a two-dimensional quantum Hamiltonian separable in Cartesian coordinates and allowing a fifthorder integral of motion. We impose the superintegrablity condition and find all doubly exotic superintegrable potentials (i.e., potentials V (x; y) = V1(x)+V2(y), where neither V1(x) nor V2(y) satisfy a linear ordinary differential equation), allowing the existence of such an integral. All of these potentials are found to have the Painleve property. Most of them are expressed in terms of known Painleve transcendents or elliptic functions but some may represent new higher order Painleve transcendents.