Time-dependent scattering theory for Schrödinger operators on scattering manifolds

Abstract

We construct a time-dependent scattering theory for Schrödinger 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.

24 pages

Cited by in corpus (2)

• On Open Scattering Channels for Manifolds with Ends
• Existence of wave operators with time-dependent modifiers for the Schödinger equations with long-range potentials on scattering manifolds