Time-dependent scattering theory for Schrödinger operators on scattering manifolds

Details Time-dependent scattering theory for Schrödinger operators on scattering manifolds Time-dependent scattering theory for Schrödinger operators on scattering manifolds

2008-10-09

arxiv.org/abs/0810.1575v1

Physics

Mathematical Physics

24 pages

Scientific paper

We construct a time-dependent scattering theory for Schr\"odinger operators on a manifold $M$ with asymptotically conic structure. We use the two-space scattering theory formalism, and a reference operator on a space of the form $R\times \partial M$, where $\partial M$ is the boundary of $M$ at infinity. We prove the existence and the completeness of the wave operators, and show that our scattering matrix is equivalent to the absolute scattering matrix, which is defined in terms of the asymptotic expansion of generalized eigenfunctions. Our method is functional analytic, and we use no microlocal analysis in this paper.

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