91 citations · 1.2k across the 114 of their papers we have counts for
5 papers · 2 filters
A family of fourth-order superintegable systems with rational potentials related to Painlevé VI
I. Marquette, S. Post, L. Ritter
We discuss a family of Hamiltonians given by particular rational extensions of the singular oscillator in two-dimensions. The wave functions of these Hamiltonians can be expressed…
Quadratic algebras as commutants of algebraic Hamiltonians in the enveloping algebra of Schrödinger algebras
Rutwig Campoamor-Stursberg, Ian Marquette
We discuss a procedure to determine finite sets within the commutant of an algebraic Hamiltonian in the enveloping algebra of a Lie algebra such that t…
-dimensional Smorodinsky-Winternitz model and related higher rank quadratic algebra
Francisco Correa, Md Fazlul Hoque, Ian Marquette +1
The -dimensional Smorodinsky-Winternitz system is a maximally superintegrable and exactly solvable model, being subject of study from different approaches. The model has been de…
Racah Algebra from Coalgebraic Structures and Chains of Substructures
Danilo Latini, Ian Marquette, Yao-Zhong Zhang
The recent interest in the study of higher-rank polynomial algebras related to -dimensional classical and quantum superintegrable systems with coalgebra symmetry and their conne…
Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials
Véronique Hussin, Ian Marquette, Kevin Zelaya
We extend and generalize the construction of Sturm-Liouville problems for a family of Hamiltonians constrained to fulfill a third-order shape-invariance condition and focusing on t…