Scattering theory for Schrödinger equations on manifolds with asymptotically polynomially growing ends

Details Scattering theory for Schrödinger equations on manifolds with asymptotically polynomially growing ends Scattering theory for Schrödinger equations on manifolds with asymptotically polynomially growing ends

2011-12-21

arxiv.org/abs/1112.5135v1

Mathematics

Analysis of PDEs

26 pages

Scientific paper

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.

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