cover the theory were written, e.g., by Fetter and Walecka [24], Linderberg and O ¨hrn [25], Mattuck [26], and Szabo
In this paper we discuss the convergence properties of the iterative solution of the inverse Dyson equation for quasiparticle correc-and Ostlund [27]. For polymers up to third-order perturbations to HF energy eigenvalues. Especially we show that this iteration theory the approach was worked out and applied by tion converges only if a principal solution exists. In this case it Liegener and Ladik [28,29]. This approach was already converges exactly to that solution. We show that a solution to which extensively studied by other groups for the case of molethe iteration converges must have a pole strength larger than and cules (see, e.g., [16][17][18][19][20][21]). A more complete list of references that this solution must be the one with the largest pole strength, because the pole strength has to have values between 0 and 1, and to work done on the correlation problem for polymers can the sum over all the pole strengths has to equal 1. As an example be found in [30], where also concepts of other research a tight binding model is discussed.