Motion in the complex plane of the poles of the quantum-mechanical partial amplitude for a bond

Details are given of the analytic features of this amplitudef _g(l, k) in the g plane for a very large class of potentials that satisfy conditions (1). It is shown that there is a region (l, k²) around the point g = 0 that is free from singularities inf _g(l, k), so the Mittag-Leffler method can be applied to findf _g(l, k) and hence also the total amplitude T_g(k, t) for any g to any specified degree of accuracy with reference to the information contained in the coefficients of a finite number of terms of the series given by perturbation methods forf _g(l, k).This paper was read in substance on 8th April 1963 at Uzhgood University 1] and on 29 June 1963 at the All-Union Symposium on the Theory of Elementary Particles at Novosibirsk.