Scattering theory for one-dimensional systems with \(\int dx\,V(x)=0\)
Low-energy scattering for Schrödinger operators of the type \(H=-\Delta \dot +V\) in \(L^ 2({\mathbb{R}})\) with \(\int_{{\mathbb{R}}}dx V(x)=0\) is considered. The possibility of zero-energy eigenstates of H is taken into account explicitly. In particular, a Laurent expansion for the transition operator and recursion relations for its coefficients are provided and the leading behaviour of the scattering operator is given in all possible cases.
scientific article; zbMATH DE number 4000573