259 citations · 3.2k across the 85 of their papers we have counts for
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Rational extensions of the Dunkl oscillator in the plane and exceptional orthogonal polynomials
C. Quesne
It is shown that rational extensions of the isotropic Dunkl oscillator in the plane can be obtained by adding some terms either to the radial equation or to the angular one obtaine…
Rationally-extended Dunkl oscillator on the line
C. Quesne
It is shown that the extensions of exactly-solvable quantum mechanical problems connected with the replacement of ordinary derivatives by Dunkl ones and with that of classical orth…
Quasi-exactly solvable extensions of the Kepler-Coulomb potential on the sphere
C. Quesne
We consider a family of extensions of the Kepler-Coulomb potential on a -dimensional sphere and analyze it in a deformed supersymmetric framework, wherein the starting potential…
Dynamical symmetry algebra of two superintegrable two-dimensional systems
Ian Marquette, Christiane Quesne
A complete classification of 2D superintegrable systems on two-dimensional conformally flat spaces has been performed over the years and 58 models, divided into 12 equivalence clas…
Minimal bosonization of double-graded supersymmetric quantum mechanics
C. Quesne
The superalgebra of -graded supersymmetric quantum mechanics is shown to be realizable in terms of a single bosonic degree of freedom. Such an approach is directly inspired…
Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. II. Three-Dimensional Model
Ian Marquette, Christiane Quesne
A shape invariant nonseparable and nondiagonalizable three-dimensional model with quadratic complex interaction was introduced by Bardavelidze, Cannata, Ioffe, and Nishnianidze. Ho…
Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model
Ian Marquette, Christiane Quesne
A shape invariant nonseparable and nondiagonalizable two-dimensional model with quadratic complex interaction, first studied by Cannata, Ioffe, and Nishnianidze, is re-examined wit…
Deformed Shape Invariant Superpotentials in Quantum Mechanics and Expansions in Powers of
C. Quesne
We show that the method developed by Gangopadhyaya, Mallow, and their coworkers to deal with (translationally) shape invariant potentials in supersymmetric quantum mechanics and co…
Revisiting generalized Hulthén potentials
C. Quesne
A relation between the deformed Hulthén potential and the Eckart one is used to write the bound-state wavefunctions of the former in terms of Jacobi polynomials and to calculate th…
Quasi-exactly solvable extended trigonometric Pöschl-Teller potentials with position-dependent mass
C. Quesne
Infinite families of quasi-exactly solvable position-dependent mass Schrödinger equations with known ground and first excited states are constructed in a deformed supersymmetric ba…
Infinite families of position-dependent mass Schrödinger equations with known ground and first excited states
C. Quesne
A construction method of infinite families of quasi-exactly solvable position-dependent mass Schrödinger equations with known ground and first excited states is proposed in a defor…
Quasi-exactly solvable Schrödinger equations, symmetric polynomials, and functional Bethe ansatz method
C. Quesne
For applications to quasi-exactly solvable Schrödinger equations in quantum mechanics, we consider the general conditions that have to be satisfied by the coefficients of a second-…
Extended Nikiforov-Uvarov method, roots of polynomial solutions, and functional Bethe ansatz method
C. Quesne
For applications to quasi-exactly solvable Schrödinger equations in quantum mechanics, we establish the general conditions that have to be satisfied by the coefficients of a second…
Connection between quantum systems involving the fourth Painleve transcendent and -step rational extensions of the harmonic oscillator related to Hermite EOP
Ian Marquette, Christiane Quesne
The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painleve transcendent P, obtained in the context o…
Deformed oscillator algebra approach of some quantum superintegrable Lissajous systems on the sphere and of their rational extensions
Ian Marquette, Christiane Quesne
We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators t…
Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials
Yves Grandati, Christiane Quesne
We construct rational extensions of the Darboux-Pöschl-Teller and isotonic potentials via two-step confluent Darboux transformations. The former are strictly isospectral to the ini…
An update on the classical and quantum harmonic oscillators on the sphere and the hyperbolic plane in polar coordinates
C. Quesne
A simple derivation of the classical solutions of a nonlinear model describing a harmonic oscillator on the sphere and the hyperbolic plane is presented in polar coordinates. These…
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…
Disconjugacy, regularity of multi-indexed rationally-extended potentials, and Laguerre exceptional polynomials
Yves Grandati, Christiane Quesne
The power of the disconjugacy properties of second-order differential equations of Schrödinger type to check the regularity of rationally-extended quantum potentials connected with…
New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials
Ian Marquette, Christiane Quesne
In recent years, many exceptional orthogonal polynomials (EOP) were introduced and used to construct new families of 1D exactly solvable quantum potentials, some of which are shape…
Revisiting (quasi-)exactly solvable rational extensions of the Morse potential
C. Quesne
The construction of rationally-extended Morse potentials is analyzed in the framework of first-order supersymmetric quantum mechanics. The known family of extended potentials $V_{A…
Rationally-extended radial oscillators and Laguerre exceptional orthogonal polynomials in kth-order SUSYQM
C. Quesne
A previous study of exactly solvable rationally-extended radial oscillator potentials and corresponding Laguerre exceptional orthogonal polynomials carried out in second-order supe…
Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions
Christiane Quesne
The -dimensional Smorodinsky-Winternitz system, proposed some years ago by Evans, is re-examined from an algebraic viewpoint. It is shown to possess a potential algebra, as well…
Exchange operator formalism for an infinite family of solvable and integrable quantum systems on a plane
C. Quesne
The exchange operator formalism in polar coordinates, previously considered for the Calogero-Marchioro-Wolfes problem, is generalized to a recently introduced, infinite family of e…