Abstract

We discuss the existence and completeness of scattering for onedimensional systems with different spatial asymptotics at ± oo, for example 2 4- V(x) where V(x) = 0 (resp. sin x) if x < 0 (resp. x> 0). We then extend our results to higher dimensional systems periodic, except for a localised impurity, in all but one space dimension. A new method, "the twisting trick", is presented for proving the absence of singular continuous spectrum, and some independent applications of this trick are given in an appendix.

Citations