Scattering is the backbone to how scientists determine everything from mass and charge to surface morphology. Stemming from classical mechanics, the quantum mechanist's scattering theory uses the similar parameters to determine not the angle of diffraction, but the probability of scattering to a (small) collection of angles. These equations today lay the foundation for Raman spectroscopy, and thus a field of light-matter interactions. resonance Raman and surface enhanced Raman being two notable examples. To gain the tools to understand a wide array of Raman tools for studying molecules--including how to create Raman active molecules--this worksheet lays out the basics of scattering theory. 
Application uses the Maple Quantum Chemistry Toolbox.