Explicit solution of a 3-d phaseless inverse scattering problem

The inverse scattering problem of the reconstruction of the unknown potential in the 3-d Schr ̈odinger equation is considered. Unlike the conventional case of an inverse scattering problem, here only the modulus of the complex valued scattered wave field is assumed to be known outside of the scatterer. The phase is unknown. This problem arises in inverse quantum scattering. Unlike the previous work of the authors, where the case of the point source was studied, here the incident plane wave is considered. An explicit solution via the inverse Radon transform is obtained.