Small angle scattering and \(X\)-ray transform in classical mechanics

DOI10.1007/BF02384831zbMath1088.70009MaRDI QIDQ1774797

Roman G. Novikov

Publication date: 19 May 2005

Published in: Arkiv för Matematik (Search for Journal in Brave)

zbMATH Keywords

uniqueness theoremNewton equationinverse scattering

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Dynamics of a system of particles, including celestial mechanics (70F99)

Related Items (14)

On inverse scattering for the multidimensional relativistic Newton equation at high energies ⋮ On inverse problems in electromagnetic field in classical mechanics at fixed energy ⋮ Inverse scattering at high energies for classical relativistic particles in a long-range electromagnetic field ⋮ An inversion formula for the attenuated \(X\)-ray transformation ⋮ Phase spaces that cannot be cloned in classical mechanics ⋮ At the interface between semiclassical analysis and numerical analysis of wave scattering problems. Abstracts from the workshop held September 25 -- October 1, 2022 ⋮ Multipoint formulas in inverse problems and their numerical implementation ⋮ High-Frequency Limit of the Inverse Scattering Problem: Asymptotic Convergence from Inverse Helmholtz to Inverse Liouville ⋮ Inverse scattering at fixed energy in de Sitter-Reissner-Nordström black holes ⋮ Equidistribution of phase shifts in semiclassical potential scattering ⋮ On inverse scattering at high energies for the multidimensional nonrelativistic Newton equation in electromagnetic field ⋮ Semiclassical limit of an inverse problem for the Schrödinger equation ⋮ On inverse scattering for the \(N\)-body Schrödinger equation ⋮ Boundary and scattering rigidity problems in the presence of a magnetic field and a potential

Cites Work

• The inverse scattering problem at fixed energy for the three-dimensional Schrödinger equation with an exponentially decreasing potential
• Inverse scattering up to smooth functions for the Schrödinger equation in one dimension
• Rapidly converging approximation in inverse quantum scattering in dimension \(2\).
• Determination of the Potential from Scattering Data
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