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.
Keywords
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