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The inverse scattering problem of the reconstruction of the unknown potentialwith compact support in the 3-d Schr\"odinger equation is considered. Only themodulus of the scattering complex valued wave field is known, whereas the phaseis unknown. It is shown that the unknown potential can be reconstructed via theinverse Radon transform. Therefore, a long standing problem posed in 1977 by K.Chadan and P.C. Sabatier in their book "Inverse Problems in Quantum ScatteringTheory" is solved.

Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrodinger equation