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.