Scattering theory has its origin in quajitum mechanics ajid is intimately related to the theory of partial differential equations. Prom mathematical point
view it caji be considered as perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. In general, perturbation theory draws conclusions a self-adjoint operator H (acting in a Hilbert space H) given aji information regarding a simpler operator Hq. Thereby it is required that the operators Hq ajid in a sense depending on a particular problem. In physical terms the operator Hq (the free Hamiltoniaji) describes a system of non-interacting particles clusters of particles), while the "full" Hamiltoniaji H describes the real system including interactions.