The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries

We review the way to analytically continue the Lippmann-Schwinger bras and kets into the complex plane. We will see that a naive analytic continuation leads to nonsensical results in resonance theory, and we will explain how the non-obvious but correct analytical continuation is done. We will see th...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2009
Main Author: de la Madrid, R.
Format: Article
Language:English
Published: Інститут математики НАН України 2009
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/149163
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries / R. de la Madrid // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 52 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-149163
record_format dspace
spelling de la Madrid, R.
2019-02-19T17:52:43Z
2019-02-19T17:52:43Z
2009
The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries / R. de la Madrid // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 52 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 81S99; 81U15
https://nasplib.isofts.kiev.ua/handle/123456789/149163
We review the way to analytically continue the Lippmann-Schwinger bras and kets into the complex plane. We will see that a naive analytic continuation leads to nonsensical results in resonance theory, and we will explain how the non-obvious but correct analytical continuation is done. We will see that the physical basis for the non-obvious but correct analytic continuation lies in the invariance of the Hamiltonian under anti-unitary symmetries such as time reversal or PT.
This paper is a contribution to the Proceedings of the VIIth Workshop “Quantum Physics with NonHermitian Operators” (June 29 – July 11, 2008, Benasque, Spain). The author wishes to thank the organizers of PHHQP VII for their kind invitation to participate in the conference and for their warm hospitality.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries
spellingShingle The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries
de la Madrid, R.
title_short The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries
title_full The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries
title_fullStr The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries
title_full_unstemmed The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries
title_sort analytic continuation of the lippmann-schwinger eigenfunctions, and antiunitary symmetries
author de la Madrid, R.
author_facet de la Madrid, R.
publishDate 2009
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description We review the way to analytically continue the Lippmann-Schwinger bras and kets into the complex plane. We will see that a naive analytic continuation leads to nonsensical results in resonance theory, and we will explain how the non-obvious but correct analytical continuation is done. We will see that the physical basis for the non-obvious but correct analytic continuation lies in the invariance of the Hamiltonian under anti-unitary symmetries such as time reversal or PT.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/149163
citation_txt The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries / R. de la Madrid // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 52 назв. — англ.
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AT delamadridr analyticcontinuationofthelippmannschwingereigenfunctionsandantiunitarysymmetries
first_indexed 2025-12-07T15:29:33Z
last_indexed 2025-12-07T15:29:33Z
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