Remarks on boundary conditions for scalar scattering

The question is discussed whether potential scattering problems can be trea ted as boundary value problems associated with differential equations, as i s sometimes suggested in the literature. We show that, except in some very special cases, this is not possible. The values of the wave function and it s normal derivative on the boundary of a finite-range potential cannot be p rescribed arbitrarily but are implicit in the integral equation of potentia l scattering. We derive two coupled singular integral equations for the bou ndary values for the case when the scattering potential is homogeneous. (C) 1998 Published by Elsevier Science B.V.