Two-centre double delta-function potential in one dimension

We have analysed the bound states in a primary one-dimensional δ-function potential perturbed by a δ-function potential at a different point, in terms of the poles of the scattering amplitude. The singularities of the pole positions correspond to the crossing of the poles, and allow us to determine the domains of convergence of the perturbation series. We have obtained the first few terms in the perturbation series for the two bound states.