Families of superintegrable Hamiltonians constructed from exceptional polynomials

Abstract

We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable.

References in corpus (2)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• An infinite family of superintegrable systems from higher order ladder operators and supersymmetry

Cited by in corpus (26)

• Classical and Quantum Superintegrability with Applications
• Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
• The Dunkl oscillator in the plane I : superintegrability, separated wavefunctions and overlap coefficients
• Two-step rational extensions of the harmonic oscillator: exceptional orthogonal polynomials and ladder operators
• New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials
• New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems
• Combined state-adding and state-deleting approaches to type III multi-step rationally-extended potentials: applications to ladder operators and superintegrability
• Integrable families of hard-core particles with unequal masses in a one-dimensional harmonic trap
• New quasi-exactly solvable class of generalized isotonic oscillators
• Shape invariance and equivalence relations for pseudowronskians of Laguerre and Jacobi polynomials
• A class of exactly solvable rationally extended Calogero-Wolfes type 3-body problems
• Higher Order Quantum Superintegrability: a new "Painlevé conjecture"
• Superintegrable deformations of superintegrable systems : Quadratic superintegrability and higher-order superintegrability
• An Algebraic Geometric Foundation for a Classification of Superintegrable Systems in Arbitrary Dimension
• Polynomial algebras of superintegrable systems separating in Cartesian coordinates from higher order ladder operators
• Superintegrability in a non-conformally-flat space
• Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials
• Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras
• A fourth-order superintegrable system with a rational potential related to Painleve VI
• The Goldilocks model of separable, zero-range, few-body interactions in one-dimensional harmonic traps
• Deformed Calogero--Moser operators and ideals of rational Cherednik algebras
• Mass-imbalanced atoms in a hard-wall trap: an exactly solvable model with emergent $D_6$ symmetry
• New families of superintegrable systems from k-step rational extensions, polynomial algebras and degeneracies
• A family of fourth-order superintegable systems with rational potentials related to Painlevé VI
• Superintegrability and Deformed Oscillator Realizations of Quantum TTW Hamiltonians on Constant-Curvature Manifolds and with Reflections in a Plane
• Impact of the non-canonical approach to the exact solution of the ideal one-dimensional electron gas confined with an anisotropic quantum wire of oscillator-shaped profile