The radial Schrödinger equation for a hydrogen-like system, in atomic units, is given by

,

with the unnormalized solutions

,

where is an associated Laguerre polynomial. Consider now a two-dimensional isotropic harmonic oscillator, expressed in polar coordinates. The associated radial Schrödinger equation takes the form

Using DSolve, we find the unnormalized solutions:

.

The solutions of the two problems can be made equivalent by the substitutions:

, , .

For selected values of and , the graphic shows plots of the radial wavefunctions and , as well as the corresponding radial distribution functions (RDFs) and .