Semiclassical Estimates for Scattering on the Real Line

We prove explicit semiclassical resolvent estimates for an integrable potential on the real line. The proof is a comparatively easy case of the spherical energies method, which has been used to prove similar theorems in higher dimensions and in more complicated geometric situations. The novelty in o...

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Bibliographic Details
Published in:Communications in mathematical physics 2020-06, Vol.376 (3), p.2301-2308
Main Authors: Datchev, Kiril, Shapiro, Jacob
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:We prove explicit semiclassical resolvent estimates for an integrable potential on the real line. The proof is a comparatively easy case of the spherical energies method, which has been used to prove similar theorems in higher dimensions and in more complicated geometric situations. The novelty in our results lies in the weakness of the assumptions on the potential.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-019-03587-1