We will illustrate the numerical solution of Schroedinger's equation by solving it for the harmonic oscillator in three dimensions. It is straightforward to change the harmonic oscillator potential with a Woods-Saxon potential, or any other type of potentials.

We are interested in the solution of the radial part of Schroedinger's equation for one nucleon. The angular momentum part is given by the so-called Spherical harmonics.

The radial equation reads $$ -\frac{\hbar^2}{2 m} \left ( \frac{1}{r^2} \frac{d}{dr} r^2 \frac{d}{dr} - \frac{l (l + 1)}{r^2} \right )R(r) + V(r) R(r) = E R(r). $$