Cancellation of the Green's function in the generation of continuum bound states by nonlocal potentials

Publisher Website
Google Scholar
Abstract
Continuum bound states (CBS) are known to appear in the spectra of some nonlocal scattering equations. We give a simple derivation of the presence of these states consistent with the requirement that such states occur for zeros of the Fredholm determinant. Examination of the form of the nonlocal potential necessary to the generation of a CBS shows that CBS solutions appear only when the potential has the effect of cancelling the Green's function in the kernel of the integral equation. Several examples from the literature are cited to demonstrate this characteristic feature of CBS.