Relations between Bound-State Problems and Scattering Theory

Abstract
An operator that takes an "unperturbed" two-particle eigenvector belonging to the discrete spectrum of a potential well of finite width into that including a short-range interaction is examined in the limit as the well width tends to infinity. It is found to approach the K operator, which satisfies the integral equation using the principal value of the kernel. The result sheds light on Brueckner's equations, which can now be formulated entirely in bound-state language. The connection between forward scattering amplitude and energy shift used in a recent paper on the π-mesonic atom is also commented on.