Scattering theory for Schrödinger equations on manifolds with asymptotically polynomially growing ends
arXiv:1112.5135
Abstract
We study a time-dependent scattering theory for Schrödinger operators on a manifold with asymptotically polynomially growing ends. We use the Mourre theory to show the spectral properties of self-adjoint second-order elliptic operators. We prove the existence and the asymptotic completeness of wave operators using the smooth perturbation theory of Kato. We also consider a two-space scattering with a simple reference system.
26 pages