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allied
academies
Journal of Applied Mathematics and Statistical Applications | Volume: 1
August 23-24, 2018 | London, UK
Applied Physics
3
rd
International Conference on
Fifth-order superintegrable quantum systems separating in Cartesian coordinates: Doubly exotic
potentials
Ismail Abouamal
University of Toronto, Canada
W
e consider a two-dimensional quantum Hamiltonian
separable in Cartesian coordinates and allowing a fifth-
order 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.
e:
ismail@math.toronto.edu