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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2009 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149163 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862670127120515072 |
|---|---|
| author | de la Madrid, R. |
| author_facet | de la Madrid, R. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T15:29:33Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149163 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:29:33Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries de la Madrid, R. |
| title | 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_short | The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries |
| title_sort | analytic continuation of the lippmann-schwinger eigenfunctions, and antiunitary symmetries |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149163 |
| work_keys_str_mv | AT delamadridr theanalyticcontinuationofthelippmannschwingereigenfunctionsandantiunitarysymmetries AT delamadridr analyticcontinuationofthelippmannschwingereigenfunctionsandantiunitarysymmetries |