91 citations · 1.2k across the 114 of their papers we have counts for
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New families of superintegrable systems from k-step rational extensions, polynomial algebras and degeneracies
Ian Marquette
Four new families of two-dimensional quantum superintegrable systems are constructed from k-step extension of the harmonic oscillator and the radial oscillator. Their wavefunctions…
Quadratic algebra structure and spectrum of a new superintegrable system in N-dimension
Md. Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
We introduce a new superintegrable Kepler-Coulomb system with non-central terms in -dimensional Euclidean space. We show this system is multiseparable and allows separation of v…
Ground-state Bethe root densities and quantum phase transitions
Jon Links, Ian Marquette
Exactly solvable models provide a unique method, via qualitative changes in the distribution of the ground-state roots of the Bethe Ansatz equations, to identify quantum phase tran…
Combined state-adding and state-deleting approaches to type III multi-step rationally-extended potentials: applications to ladder operators and superintegrability
Ian Marquette, Christiane Quesne
Type III multi-step rationally-extended harmonic oscillator and radial harmonic oscillator potentials, characterized by a set of integers , , \ldots, , such that…
On realizations of polynomial algebras with three generators via deformed oscillator algebras
Phillip S. Isaac, Ian Marquette
We present the most general polynomial Lie algebra generated by a second order integral of motion and one of order M, construct the Casimir operator, and show how the Jacobi identi…
New quasi-exactly solvable class of generalized isotonic oscillators
Davids Agboola, Jon Links, Ian Marquette +1
We introduce a new family of quasi-exactly solvable generalized isotonic oscillators which are based on the pseudo-Hermite exceptional orthogonal polynomials. We obtain exact close…