English

Free Oscillator Realization of the Laguerre Polynomial

Mathematical Physics 2022-02-09 v2 High Energy Physics - Theory Classical Analysis and ODEs math.MP Exactly Solvable and Integrable Systems

Abstract

We revisit the radial oscillator from the free oscillator realization point of view. By using a free oscillator, namely the creation/annihilation operators of the harmonic oscillator, we construct an operator that maps the eigenfunctions of the harmonic oscillator to those of the radial oscillator. As a polynomial part of this relation, we obtain an operator that maps the Hermite polynomials to the Laguerre polynomials.

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Cite

@article{arxiv.2008.10756,
  title  = {Free Oscillator Realization of the Laguerre Polynomial},
  author = {Satoru Odake},
  journal= {arXiv preprint arXiv:2008.10756},
  year   = {2022}
}

Comments

8 pages. Abstract is changed