91 citations · 1.2k across the 114 of their papers we have counts for
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Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator
Scott E. Hoffmann, Véronique Hussin, Ian Marquette +1
We construct ladder operators, and , for a multi-step rational extension of the harmonic oscillator on the half plane, . These ladder operator…
Two-dimensional superintegrable systems from operator algebras in one dimension
Ian Marquette, Masoumeh Sajedi, Pavel Winternitz
We develop new constructions of 2D classical and quantum superintegrable Hamiltonians allowing separation of variables in Cartesian coordinates. In classical mechanics we start fro…
Extended Laplace-Runge-Lentz vectors, new family of superintegrable systems and quadratic algebras
Zhe Chen, Ian Marquette, Yao-Zhong Zhang
We present a useful proposition for discovering extended Laplace-Runge-Lentz vectors of certain quantum mechanical systems. We propose a new family of superintegrable systems and c…
On Casimir Operators of Conformal Galilei Algebras
Fahad Alshammari, Phillip S. Isaac, Ian Marquette
In previous work, we introduced an algorithm that utilises differential operator realisations to find polynomial Casimir operators of Lie algebras. In this article we build on this…
Coherent states for ladder operators of general order related to exceptional orthogonal polynomials
Scott E. Hoffmann, Véronique Hussin, Ian Marquette +1
We construct the coherent states of general order, for the ladder operators, and , which act on rational deformations of the harmonic oscillator. The posit…
On superintegrable monopole systems
Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
Superintegrable systems with monopole interactions in flat and curved spaces have attracted much attention. For example, models in spaces with a Taub-NUT metric are well-known to a…