An infinite family of superintegrable Hamiltonians with reflection in the plane

Abstract

We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schrödinger equations admit separation of variables in polar coordinates and are exactly solvable. The angular part of the wave function is expressed in terms of little -1 Jacobi polynomials. The spectra exhibit "accidental" degeneracies. The superintegrability of the model is proved using the recurrence relation approach. The (higher-order) constants of motion are constructed and the structure equations of the symmetry algebra obtained.

19 pages

References in corpus (6)

• A Recurrence Relation Approach to Higher Order Quantum Superintegrability
• Supersymmetric Quantum Mechanics with Reflections
• An infinite family of superintegrable systems from higher order ladder operators and supersymmetry
• From $s{l}_q(2)$ to a Parabosonic Hopf Algebra
• A Bochner Theorem for Dunkl Polynomials
• Jordan algebras and orthogonal polynomials

Cited by in corpus (6)

• Fourth order superintegrable systems separating in Polar Coordinates. I. Exotic Potentials
• Infinite families of superintegrable systems separable in subgroup coordinates
• A class of exactly solvable rationally extended Calogero-Wolfes type 3-body problems
• Superintegrability in a non-conformally-flat space
• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
• Superintegrability and Deformed Oscillator Realizations of Quantum TTW Hamiltonians on Constant-Curvature Manifolds and with Reflections in a Plane