2014/12/28 by Michael V. Klibanov, Klibanov, Michael V., V. G. Romanov +1
Mathematics · Physics and Astronomy · #Advanced X-ray Imaging Techniques #Crystallography and Radiation Phenomena #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1412.8210
openalex publication_date 2014/12/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The inverse scattering problem of the reconstruction of the unknown potential with compact support in the 3-d Schrödinger equation is considered. Only the modulus of the scattering complex valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. Therefore, a long standing problem posed in 1977 by K. Chadan and P.C. Sabatier in their book "Inverse Problems in Quantum Scattering Theory" is solved.