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 the separation of variables in polar coordinates and are exactly solvable. The angular part of the wavefunction 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 are obtained.