Phaseless inverse scattering in the one-dimensional case

Roman Novikov (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We consider the one-dimensional Schrödinger equation with a potential satisfying the standard assumptions of the inverse scattering theory and supported on the half-line x ≥ 0. For this equation at fixed positive energy we give explicit formulas for finding the full complex valued reflection coefficient to the left from appropriate phaseless scattering data measured on the left, i.e. for x < 0. Using these formulas and known inverse scattering results we obtain global uniqueness and reconstruction results for phaseless inverse scattering in dimension d = 1.

Domaines: Physique mathématique [math-ph]

Roman Novikov. Phaseless inverse scattering in the one-dimensional case. Eurasian Journal of Mathematical and Computer Applications, 2015, 3 (1), pp.64-70. ⟨hal-01124441⟩