dorsal/arxiv
View SchemaThe rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets
| Authors | R. de la Madrid |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603177 |
| URL | https://arxiv.org/abs/quant-ph/0603177 |
| DOI | 10.1088/0305-4470/39/15/009 |
| Journal | J. Phys. A: Math. Gen. 39 (2006) 3981-4009 |
Abstract
The analytic continuation of the Lippmann-Schwinger bras and kets is obtained and characterized. It is shown that the natural mathematical setting for the analytic continuation of the solutions of the Lippmann-Schwinger equation is the rigged Hilbert space rather than just the Hilbert space. It is also argued that this analytic continuation entails the imposition of a time asymmetric boundary condition upon the group time evolution, resulting into a semigroup time evolution. Physically, the semigroup time evolution is simply a (retarded or advanced) propagator.
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"abstract": "The analytic continuation of the Lippmann-Schwinger bras and kets is obtained\nand characterized. It is shown that the natural mathematical setting for the\nanalytic continuation of the solutions of the Lippmann-Schwinger equation is\nthe rigged Hilbert space rather than just the Hilbert space. It is also argued\nthat this analytic continuation entails the imposition of a time asymmetric\nboundary condition upon the group time evolution, resulting into a semigroup\ntime evolution. Physically, the semigroup time evolution is simply a (retarded\nor advanced) propagator.",
"arxiv_id": "quant-ph/0603177",
"authors": [
"R. de la Madrid"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1088/0305-4470/39/15/009",
"journal_ref": "J. Phys. A: Math. Gen. 39 (2006) 3981-4009",
"title": "The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets",
"url": "https://arxiv.org/abs/quant-ph/0603177"
},
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