Renormalized two-body low-energy scattering

Details Renormalized two-body low-energy scattering Renormalized two-body low-energy scattering

2012-03-28

arxiv.org/abs/1203.6197v1

Physics

Mathematical Physics

Scientific paper

For a class of long-range potentials, including ultra-strong perturbations of the attractive Coulomb potential in dimension $d\geq3$, we introduce a stationary scattering theory for Schr\"odinger operators which is regular at zero energy. In particular it is well defined at this energy, and we use it to establish a characterization there of the set of generalized eigenfunctions in an appropriately adapted Besov space generalizing parts of \cite{DS3}. Principal tools include global solutions to the eikonal equation and strong radiation condition bounds.

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