91 citations · 1.2k across the 114 of their papers we have counts for
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Non-linear ladder operators and coherent states for the 2:1 oscillator
James Moran, Véronique Hussin, Ian Marquette
The 2:1 two-dimensional anisotropic quantum harmonic oscillator is considered and new sets of states are defined by means of normal-ordering non-linear operators through the use of…
Embedding of the Racah Algebra R() and Superintegrability
Danilo Latini, Ian Marquette, Yao-Zhong Zhang
The rank- Racah algebra plays a pivotal role in the theory of superintegrable systems. It appears as the symmetry algebra of the -parameter system on the -sphere fr…
Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. II. Three-Dimensional Model
Ian Marquette, Christiane Quesne
A shape invariant nonseparable and nondiagonalizable three-dimensional model with quadratic complex interaction was introduced by Bardavelidze, Cannata, Ioffe, and Nishnianidze. Ho…
Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model
Ian Marquette, Christiane Quesne
A shape invariant nonseparable and nondiagonalizable two-dimensional model with quadratic complex interaction, first studied by Cannata, Ioffe, and Nishnianidze, is re-examined wit…
Hidden symmetry algebra and construction of quadratic algebras of superintegrable systems
Rutwig Campoamor-Stursberg, Ian Marquette
The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials tha…
Polynomial algebras from and the generic model on the two sphere
Francisco Correa, Mariano A. del Olmo, Ian Marquette +1
Construction of superintegrable systems based on Lie algebras have been introduced over the years. However, these approaches depend on explicit realisations, for instance as a diff…