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arXiv · 1303.7150

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

I. Marquette·C. Quesne
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Abstract

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.

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I. Marquette, C. Quesne. 2013-03-28. New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems. https://doi.org/10.1063/1.4823771

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