The Schrodinger operator in the plane

The delta method of scattering and inverse scattering is adapted to the Schrodinger operator delta ²/ delta zeta ²+ delta ²/ delta eta ²-q( zeta , eta ) in R² with small potential q( zeta , eta ). Eigenfunctions of eigenvalue zero are studied. One may determine the delta scattering data from the leading coefficients of the asymptotic expansions of these eigenfunctions at large values of ( zeta , eta ) or by taking the delta _z derivatives of these eigenfunctions. There are four scattering data to be used to solve the inverse problem but they can be reduced to one. The relations between small potentials and small delta scattering data are discussed.