Scattering theory for the Klein-Gordon equation

AbstractWe develop the scattering theory for the Klein-Gordon equation. We follow the usual procedure of considering an equivalent equation, which is first order in time, in the Hilbert space of vector valued functions which have a finite energy norm. We prove existence and completeness of the wave operators, the intertwining relations, and the invariance principle as well. This is done for a large class of potentials. In particular, the magnetic potential may even be divergent at infinity. Electric and scalar potentials that behave at infinity as ¦x¦−ϵ − l, ϵ > 0 are contained in our class