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

par Marquette, Ian;Quesne, Christiane
Référence Journal of mathematical physics, 54, 10, 102102
Publication Publié, 2013-10

Article révisé par les pairs

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Résumé :

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. © 2013 AIP Publishing LLC.