Scattering theory for Schr\"{o}dinger equations on manifolds with   asymptotically polynomially growing ends
  We study a time-dependent scattering theory for Schr\"{o}dinger 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. 
Shinichiro Itozaki
math.AP math-ph math.MP