Convergence of the Born series

John V. Corbett*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)891-898
Number of pages8
JournalJournal of Mathematical Physics
Issue number6
Publication statusPublished - 1968
Externally publishedYes

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