Scattering Theory (Methods of Modern Mathematical Physics Vol. 3)

About this book

Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself. As such it is the most effective means sometimes the only means to study microscopic nature. To understand the importance of scattering theory consider the variety of ways in which it arises. First there are various phenomena in nature (like the blue of the sky) which are the result of scattering. In order to understand the phenomenon (and to identify it as the result of scattering) one must understand the underlying dynamics and its scattering theory. Second one often wants to use the scattering of waves or particles whose dynamics on knows to determine the structure and position of small or inaccessible objects. For example in x-ray crystallography (which led to the discovery of DNA) tomography and the detection of underwater objects by sonar the underlying dynamics is well understood. What one would like to construct are correspondences that link via the dynamics the position shape and internal structure of the object to the scattering data. Ideally the correspondence should be an explicit formula which allows one to reconstruct at least approximately the object from the scattering data. The main test of any proposed particle dynamics is whether one can construct for the dynamics a scattering theory that predicts the observed experimental data. Scattering theory was not always so central the physics. Even thought the Coulomb cross section could have been computed by Newton had he bothered to ask the right question its calculation is generally attributed to Rutherford more than two hundred years later. Of course Rutherfords calculation was in connection with the first experiment in nuclear physics.