Distribution of poles for scattering on the real line (Q1113349)

The density of scattering poles is shown to be proportional to the length of the convex hull of the support of the potential. In the case of a potential with finite singularities at the endpoints of the support, asymptotic formulae for the poles are given, while in the \(C^{\infty}_0\) case, an example of a potential with infinitely many scattering poles on \({\mathbb{R}}\) is constructed. The scattering amplitude of a compactly supported potential is also characterized.