Potentials with identical scattering properties below a critical energy

Abstract

A pair of scattering potentials are called alpha-equivalent if they have identical scattering properties for incident plane waves with wavenumber k <= alpha (energy k(2) <= alpha(2)). We use a recently developed multidimensional transfer-matrix formulation of scattering theory to obtain a simple criterion for alpha-equivalence of complex potentials in two and three dimensions.