91 citations · 1.2k across the 114 of their papers we have counts for
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Hidden symmetry and Jordan chains in a resonant ghostly three-dimensional model
Andreas Fring, Ian Marquette
We investigate a three-dimensional ghostly Hamiltonian realisation of the fully degenerate resonant sixth-order Pais-Uhlenbeck oscillator. On the classical level, the phase-space f…
Spectrum-generating algebra and intertwiners of the resonant Pais-Uhlenbeck oscillator
Andreas Fring, Ian Marquette, Takano Taira
We study the quantum Pais-Uhlenbeck oscillator at the resonant (equal-frequency) point, where the dynamics becomes non-diagonalisable and the conventional Fock-space construction c…
Generalized quantum Zernike Hamiltonians: Polynomial Higgs-type algebras and algebraic derivation of the spectrum
Rutwig Campoamor-Stursberg, Francisco J. Herranz, Danilo Latini +2
We consider the quantum analog of the generalized Zernike systems given by the Hamiltonian: $$\hat{\mathcal{H}}_N =\hat{p}_1^2+\hat{p}_2^2+\sum_{k=1}^N γ_k (\hat{q}_1 \hat{p}_1+\ha…
Algebraic construction of associated functions of nondiagonalizable models with anharmonic oscillator complex interaction
I. Marquette, C. Quesne
A shape invariant nonseparable and nondiagonalizable two-dimensional model with anharmonic complex interaction, first studied by Cannata, Ioffe, and Nishnianidze, is re-examined wi…
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…
Fourth Painlevé and Ermakov equations: quantum invariants and new exactly-solvable time-dependent Hamiltonians
Kevin Zelaya, Ian Marquette, Véronique Hussin
In this work, we introduce a new realization of exactly-solvable time-dependent Hamiltonians based on the solutions of the fourth Painlevé and the Ermakov equations. The latter is…