We are first interested in the solution of the radial part of Schroedinger's equation for one electron. This equation reads $$-\frac{\hbar^2}{2 m} \left ( \frac{1}{r^2} \frac{d}{dr} r^2 \frac{d}{dr} - \frac{l (l + 1)}{r^2} \right )R(r) + V(r) R(r) = E R(r).$$ In our case $V(r)$ is the harmonic oscillator potential $(1/2)kr^2$ with $k=m\omega^2$ and $E$ is the energy of the harmonic oscillator in three dimensions. The oscillator frequency is $\omega$ and the energies are $$E_{nl}= \hbar \omega \left(2n+l+\frac{3}{2}\right),$$ with $n=0,1,2,\dots$ and $l=0,1,2,\dots$.