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

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

2006-03-20

arxiv.org/abs/quant-ph/0603176v1

J. Phys. A: Math. Gen. 39 (2006) 3949-3979

Physics

Quantum Physics

34 pages, 1 figure

Scientific paper

10.1088/0305-4470/39/15/008

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.

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