91 citations · 1.2k across the 114 of their papers we have counts for
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A new approach to analysis of 2D higher order quantum superintegrable systems
Bjorn K. Berntson, Ian Marquette, Willard Miller
We revise a method by Kalnins, Kress and Miller (2010) for constructing a canonical form for symmetry operators of arbitrary order for the Schrödinger eigenvalue equation $HΨ\equiv…
Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras
Zhe Chen, Ian Marquette, Yao-Zhong Zhang
We present a new method for constructing -dimensional minimally superintegrable systems based on block coordinate separation of variables. We give two new families of superinteg…
Higher order superintegrability, Painlevé transcendents and representations of polynomial algebras
Ian Marquette
In recent years, progress toward the classification of superintegrable systems with higher order integrals of motion has been made. In particular, a complete classification of all…
Generalized conformal pseudo-Galilean algebras and their Casimir operators
Rutwig Campoamor-Stursberg, Ian Marquette
A generalization of the conformal Galilei algebra with Levi subalgebra isomorphic to $\mathfrak{sl}(2,\mathbb{R})\oplus\mathfr…
Higher Order Quantum Superintegrability: a new "Painlevé conjecture"
Ian Marquette, Pavel Winternitz
We review recent results on superintegrable quantum systems in a two-dimensional Euclidean space with the following properties. They are integrable because they allow the separatio…