Different faces of harmonic oscillator

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Harmonic oscillator in Fock space is defined. Isospectral as well as polynomiality-of-eigenfunctions preserving, translation-invariant discretization of the harmonic oscillator is presented. Dilatation-invariant and polynomiality-of-eigenfunctions preserving discretization is also given.
9pp, AMSTeX, Contribution to the Proceedings of the Conference SIDE III,Roma, Italy, May 1998, to be published by CRM Press, Canada

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