Almost all we see and perceive comes to us indirectly by the scattering of light from various objects; that is, by the scattering of electromagnetic radiation over a very restricted interval of the frequency spectrum. Much of this merely illuminates our world and helps us move about, while some exceptional natural scattering phenomena such as rainbows, glories, and halos touch our aesthetic sense. On a technical level, a very large portion of what we have learned about the physical world over the past four millennia has come to us via scattering experiments with both particles and waves, so that a study of scattering theory is an integral part of physics itself.

Classically the most familiar type of scattering is that among particles, such as balls on a pool table – or, more deeply, among gas molecules in the room where we work. Equally evident, however, are the results of scattering of electromagnetic and sound waves, and at first these appear to be entirely different phenomena. Just as modern quantum theory has compelled us to view all matter in terms of a particle–wave dichotomy, however, so have we also learned to view scattering processes as both particle-like and wave-like. That is, at high frequencies and short wavelengths even intrinsically wave-like classical phenomena exhibit particle-like scattering behavior, whereas on the quantum level particle scattering usually must be viewed in terms of waves.