5 citations · 11 across the 10 of their papers we have counts for
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On polynomial symmetry algebras underlying superintegrable systems in Darboux spaces
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
We review three different approaches to polynomial symmetry algebras underlying superintegrable systems in Darboux spaces. The first method consists of using deformed oscillator al…
Algebraic structures and Hamiltonians from the equivalence classes of 2D conformal algebras
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
The construction of superintegrable systems based on Lie algebras and their universal enveloping algebras has been widely studied over the past decades. However, most constructions…
Infinite dimensional representations of cubic and quintic algebras and special functions
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we intr…
Algebraic approach and exact solutions of superintegrable systems in 2D Darboux spaces
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
Superintegrable systems in 2D Darboux spaces were classified and it was found that there exist 12 distinct classes of superintegrable systems with quadratic integrals of motion (an…