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arXiv:1112.5135 [math.AP]AbstractReferencesReviewsResources

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

Shinichiro Itozaki

Published 2011-12-21Version 1

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.

Comments: 26 pages
Categories: math.AP, math-ph, math.MP
Subjects: 58J50, 35P25, 81U05
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