  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.
