Different faces of harmonic oscillator

@article{Turbiner1999DifferentFO,
  title={Different faces of harmonic oscillator},
  author={Alexander V. Turbiner},
  journal={arXiv: Mathematical Physics},
  year={1999}
}
  • A. Turbiner
  • Published 9 May 1999
  • Computer Science
  • arXiv: Mathematical Physics
Harmonic oscillator in Fock space is defined. Isospectral as well as polynomiality-of-eigenfunctions preserving, translation-invariant discretization of the harmonic oscillator is presented. Dilatationinvariant and polynomiality-of-eigenfunctions preserving discretization is also given. 

Umbral calculus, difference equations and the discrete Schrödinger equation

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