2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220446We prove that the singularities of a potential in the two and three dimensional Schrödinger equation are the same as the singularities of the Born approximation (Diffraction Tomography), obtained from backscattering inverse data, with an accuracy of $1/2^-$ derivative in the scale of $L^2$-based Sobolev spaces. The key point is the study of the smoothing properties of the quartic term in the Neumann-Born expansion of the scattering amplitude in 3D, together with a Leibniz formula for multiple scattering valid in any dimension.33 pagesAnalysis of PDEs35Q40text