Abstract
For a class of long-range potentials, including ultra-strong perturbations of the attractive Coulomb potential in dimension d ≥ 3, we introduce a stationary scattering theory for Schrödinger 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 [DS1]. Principal tools include global solutions of the eikonal equation and strong radiation condition bounds.
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Skibsted, E. Renormalized two-body low-energy scattering. JAMA 122, 25–68 (2014). https://doi.org/10.1007/s11854-014-0002-0
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DOI: https://doi.org/10.1007/s11854-014-0002-0