The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I

Abstract

We exemplify the way the rigged Hilbert space deals with the Lippmann-Schwinger equation by way of the spherical shell potential. We explicitly construct the Lippmann-Schwinger bras and kets along with their energy representation, their time evolution and the rigged Hilbert spaces to which they belong. It will be concluded that the natural setting for the solutions of the Lippmann-Schwinger equation--and therefore for scattering theory--is the rigged Hilbert space rather than just the Hilbert space.

arXiv comment34 pages, 1 figure

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Cited by in corpus (5)

• The rigged Hilbert space approach to the Gamow states
• The resonance amplitude associated with the Gamow states
• The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets
• On the inconsistency of the Bohm-Gadella theory with quantum mechanics
• Reply to ``Comment on `On the inconsistency of the Bohm-Gadella theory with quantum mechanics'''