1303.7150 (I. Marquette et al.)

New ladder operators for a rational extension of the harmonic oscillator
and superintegrability of some two-dimensional systems    [PDF]

I. Marquette, C. Quesne

New ladder operators are constructed for a rational extension of the harmonic oscillator associated with type III Hermite exceptional orthogonal polynomials and characterized by an even integer $m$. The eigenstates of the Hamiltonian separate into $m+1$ infinite-dimensional unitary irreducible representations of the corresponding polynomial Heisenberg algebra. These ladder operators are used to construct a higher-order integral of motion for two superintegrable two-dimensional systems separable in cartesian coordinates. The polynomial algebras of such systems provide for the first time an algebraic derivation of the whole spectrum through their finite-dimensional unitary irreducible representations.

View original: http://arxiv.org/abs/1303.7150