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

Shinichiro Itozaki

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arXiv · 1112.5135

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

Shinichiro Itozaki

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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.

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Shinichiro Itozaki. 2011-12-21. Scattering theory for Schrödinger equations on manifolds with asymptotically polynomially growing ends. https://arxiv.org/abs/1112.5135

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