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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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2009-04-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2009.043 |
| _version_ | 1811343098549108736 |
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| author | Rafael de la Madrid |
| author_facet | Rafael de la Madrid |
| author_sort | Rafael de la Madrid |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-13T19:23:41Z |
| format | Article |
| id | doaj.art-9b9515eb76b74857abd286c338fbddcb |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-04-13T19:23:41Z |
| publishDate | 2009-04-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-9b9515eb76b74857abd286c338fbddcb2022-12-22T02:33:27ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592009-04-015043The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary SymmetriesRafael de la MadridWe 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.http://dx.doi.org/10.3842/SIGMA.2009.043Lippmann-Schwinger equationresonancesGamow statesresonant expansionstime reversalPT symmetry |
| spellingShingle | Rafael de la Madrid The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries Symmetry, Integrability and Geometry: Methods and Applications Lippmann-Schwinger equation resonances Gamow states resonant expansions time reversal PT symmetry |
| 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 |
| topic | Lippmann-Schwinger equation resonances Gamow states resonant expansions time reversal PT symmetry |
| url | http://dx.doi.org/10.3842/SIGMA.2009.043 |
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