THE SCHRODINGER OPERATOR IN THE PLANE

The partial-derivativeBAR method of scattering and inverse scattering is adapted to the Schrodinger operator partial-derivative2/partial-der ivative zeta2 + partial-derivative2/partial-derivative eta2 - q(zeta, eta) in R2 with small potential q(zeta, eta). Eigenfunctions of eigenv alue zero are studied. One may determine the 5 scattering data from th e leading coefficients of the asymptotic expansions of these eigenfunc tions at large values of (zeta, eta) or by taking the partial-derivati ve(zBAR) derivatives of these eigenfunctions. There are four scatterin g data to be used to solve the inverse problem but they can be reduced to one. The relations between small potentials and small partial-deri vativeBAR scattering data are discussed.