Editing Scattering (section)

==Theoretical physics==
[[Image:Scattering theory illust.png|right|thumb|Top: the [[real part]] of a [[plane wave]] travelling upwards. Bottom: The real part of the field after inserting in the path of the plane wave a small transparent disk of [[index of refraction]] higher than the index of the surrounding medium. This object scatters part of the wave field, although at any individual point, the wave's frequency and wavelength remain intact.]]
In [[mathematical physics]], '''scattering theory''' is a framework for studying and understanding the interaction or scattering of solutions to [[partial differential equation]]s. In [[acoustics]], the differential equation is the [[wave equation]], and scattering studies how its solutions, the [[sound wave]]s, scatter from solid objects or propagate through non-uniform media (such as sound waves, in [[sea water]], coming from a [[submarine]]). In the case of classical [[electrodynamics]], the differential equation is again the wave equation, and the scattering of [[light]] or [[radio wave]]s is studied. In [[particle physics]], the equations are those of [[Quantum electrodynamics]], [[Quantum chromodynamics]] and the [[Standard Model]], the solutions of which correspond to  [[fundamental particle]]s.

In regular [[quantum mechanics]], which includes [[quantum chemistry]], the relevant equation is the [[Schrödinger equation]], although equivalent formulations, such as the [[Lippmann-Schwinger equation]] and the [[Faddeev equation]]s, are also largely used. The solutions of interest describe the long-term motion of free atoms, molecules, photons, electrons, and protons. The scenario is that several particles come together from an infinite distance away. These reagents then collide, optionally reacting, getting destroyed or creating new particles. The products and unused reagents then fly away to infinity again. (The atoms and molecules are effectively particles for our purposes. Also, under everyday circumstances, only photons are being created and destroyed.) The solutions reveal which directions the products are most likely to fly off to and how quickly. They also reveal the probability of various reactions, creations, and decays occurring. There are two predominant techniques of finding solutions to scattering problems: [[partial wave analysis]], and the [[Born approximation]].