Motion in the complex plane of the poles of the quantummechanical partial amplitude for a bond
Abstract
Details are given of the analytic features of this amplitude f _{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 ɛ( l, k^{2}) around the point g = 0 that is free from singularities in f _{g}( l, k), so the MittagLeffler method can be applied to find f _{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 for f _{g}( l, k).
 Publication:

Soviet Physics Journal
 Pub Date:
 May 1965
 DOI:
 10.1007/BF00827919
 Bibcode:
 1965SvPhJ...8c..58L