Scattering and inverse scattering for multipoint potentials at high energies

Abstract We consider the solvable Schrödinger equation with a multipoint potential of Bethe–Peierls–Thomas–Fermi type. For this singular potential, we develop scattering and inverse scattering at high energies. In particular, in this framework, our results include analogs of the “regular” Born–Faddeev formula for the scattering amplitude and analogs of related “regular” inverse scattering reconstructions at high energies. Related results for scattering solutions at high energies are also presented.