Three types of Born series which can be associated with a transition amplitude are discussed, and the criteria for the convergence of the different series are compared. With regard to the divergence of the Born series, the ordering, matrix-element series diverges implies vector series diverges implies operator series diverges, is obtained for the natural vector and operator Born series that can be abstracted from the expression for the transition amplitude. The conclusion that the divergence of the operator Born series does not ensure that the Born series of physical matrix-elements divergences is applied to an example of three-body rearrangement scattering.
|Number of pages||8|
|Journal||Journal of Mathematical Physics|
|Publication status||Published - 1968|