91 citations · 1.2k across the 114 of their papers we have counts for
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Nested polynomial algebras and the exact spectrum of a three-dimensional two-spin oscillator
Ian Marquette, O. Ogulcan Tuncer, I. Yurdusen
We construct representations of the symmetry algebra and derive the exact spectrum of a three-dimensional oscillator with two spin- degrees of freedom. The Hamiltonian an…
Superintegrable systems in curved spaces via coalgebras and deformed Racah algebras
Samuel Jimenez-Swain, Ian Marquette, Yao-Zhong Zhang
We determine the Poisson algebras generated by partial Casimirs of undeformed and non-standard -deformed coalgebras, respectively. The derivation is performed…
Superintegrability of a resonant ghostly tri-Hamiltonian model: polynomial first integrals and transcendental completion
Andreas Fring, Ian Marquette
We study classical and quantum superintegrability of a resonant three-dimensional Hamiltonian with indefinite kinetic energy and three Poisson descriptions of the same flow. Beside…
Quadratic symmetry algebras and Sturm algebraization of superintegrable systems with magnetic fields
Shams Ara, Md Fazlul Hoque, Ian Marquette
We study two three-dimensional quantum superintegrable systems in nonvanishing axially symmetric magnetic fields. For each model the integrals generate a quadratic algebra with a C…
Quasi-exactly solvable deformations of quantum systems associated with exceptional orthogonal polynomials
Siyu Li, Ian Marquette, Sarah Post +1
Quasi-exactly solvable (QES) deformations of harmonic and singular oscillators have been widely studied via a range of approaches. In this paper, we obtain families of new QES defo…
Geometric construction of superintegrable Poisson projection chains via Poisson centralizers
Kai Jiang, Guorui Ma, Ian Marquette +2
We introduce a geometric framework for constructing superintegrable systems from Poisson centralizers (commutants) in the Lie-Poisson algebra of a complex semisim…