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arXiv · 1104.0294

Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions

Christiane Quesne
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Abstract

The $D$-dimensional Smorodinsky-Winternitz system, proposed some years ago by Evans, is re-examined from an algebraic viewpoint. It is shown to possess a potential algebra, as well as a dynamical potential one, in addition to its known symmetry and dynamical algebras. The first two are obtained in hyperspherical coordinates by introducing $D$ auxiliary continuous variables and by reducing a 2D-dimensional harmonic oscillator Hamiltonian. The su(2D) symmetry and ${\rm w}(2D) \oplus_s {\rm sp}(4D,{\mathbb R})$ dynamical algebras of this Hamiltonian are then transformed into the searched for potential and dynamical potential algebras of the Smorodinsky-Winternitz system. The action of generators on wavefunctions is given in explicit form for D=2.

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Christiane Quesne. 2011-04-02. Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions. https://doi.org/10.3842/sigma.2011.035

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