Classical and quantum superintegrability with applications
W Miller, S Post, P Winternitz - Journal of Physics A: Mathematical …, 2013 - iopscience.iop.org
A superintegrable system is, roughly speaking, a system that allows more integrals of motion
than degrees of freedom. This review is devoted to finite dimensional classical and quantum …
than degrees of freedom. This review is devoted to finite dimensional classical and quantum …
Families of superintegrable Hamiltonians constructed from exceptional polynomials
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave
functions are given in terms of Laguerre and exceptional Jacobi polynomials. The …
functions are given in terms of Laguerre and exceptional Jacobi polynomials. The …
General Nth-order superintegrable systems separating in polar coordinates
AM Escobar-Ruiz, P Winternitz… - Journal of Physics A …, 2018 - iopscience.iop.org
The general description of superintegrable systems with one polynomial integral of order N
in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean plane …
in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean plane …
General Nth order integrals of motion in the Euclidean plane
S Post, P Winternitz - Journal of Physics A: Mathematical and …, 2015 - iopscience.iop.org
The general form of an integral of motion that is a polynomial of order N in the momenta is
presented for a Hamiltonian system in two-dimensional Euclidean space. The classical and …
presented for a Hamiltonian system in two-dimensional Euclidean space. The classical and …
A recurrence relation approach to higher order quantum superintegrability
EG Kalnins, JM Kress, W Miller - SIGMA. Symmetry, Integrability and …, 2011 - emis.de
We develop our method to prove quantum superintegrability of an integrable 2D system,
based on recurrence relations obeyed by the eigenfunctions of the system with respect to …
based on recurrence relations obeyed by the eigenfunctions of the system with respect to …
Superintegrability of generalized Calogero models with oscillator or Coulomb potential
We deform N-dimensional (Euclidean, spherical and hyperbolic) oscillator and Coulomb
systems, replacing their angular degrees of freedom by those of a generalized rational …
systems, replacing their angular degrees of freedom by those of a generalized rational …
Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere
EG Kalnins, W Miller, S Post - SIGMA. Symmetry, Integrability and …, 2011 - emis.de
We show that the symmetry operators for the quantum superintegrable system on the 3-
sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly …
sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly …
A nonseparable quantum superintegrable system in 2D real Euclidean space
S Post, P Winternitz - Journal of Physics A: Mathematical and …, 2011 - iopscience.iop.org
In this paper, we derive a nonseparable quantum superintegrable system in 2D real
Euclidean space. The Hamiltonian admits no second-order integrals of motion but does …
Euclidean space. The Hamiltonian admits no second-order integrals of motion but does …
Higher Order Quantum Superintegrability: A New “Painlevé Conjecture” Higher Order Quantum Superintegrability
I Marquette, P Winternitz - … Supersymmetry and Coherent States: A Volume …, 2019 - Springer
We review recent results on superintegrable quantum systems in a two-dimensional
Euclidean space with the following properties. They are integrable because they allow the …
Euclidean space with the following properties. They are integrable because they allow the …
Higher order superintegrability of separable potentials with a new approach to the Post–Winternitz system
MF Ranada - Journal of Physics A: Mathematical and Theoretical, 2013 - iopscience.iop.org
The higher order superintegrability of separable potentials is studied. It is proved that these
potentials possess (in addition to the two quadratic integrals) a third integral of higher order …
potentials possess (in addition to the two quadratic integrals) a third integral of higher order …