The contribution of bound states to the polarizability of a hydrogen atom in the ground state is explained in this note and computed in this Mathematica notebook.
Here is a note on Continuum Wave Functions, with a Mathematica notebook to plot the nodes of the free-particle and Coulomb standing waves.
Here is an animation of the scattering of a plane wave by an impenetrable sphere, together with the drawings of some partial waves (and the Mathematica notebook used to produce it, which also contains partial waves, the scattering cross section and the free particle case).