Non-adiabatic quantum evolution: The S matrix as a geometrical phase factor
We present a complete derivation of the exact evolution of quantum mechanics for the case when the underlying spectrum is continuous. We base our discussion on the use of the Weyl eigendifferentials. We show that a quantum system being in an eigenstate of an invariant will remain in the subspace gen...
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| Veröffentlicht in: | Physics letters. A 2012-03, Vol.376 (16), p.1328-1334 |
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| container_title | Physics letters. A |
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| creator | Saadi, Y. Maamache, M. |
| description | We present a complete derivation of the exact evolution of quantum mechanics for the case when the underlying spectrum is continuous. We base our discussion on the use of the Weyl eigendifferentials. We show that a quantum system being in an eigenstate of an invariant will remain in the subspace generated by the eigenstates of the invariant, thereby acquiring a generalized non-adiabatic or Aharonov–Anandan geometric phase linked to the diagonal element of the S matrix. The modified Pöschl–Teller potential and the time-dependent linear potential are worked out as illustrations.
► In this Letter we study the exact quantum evolution for continuous spectra problems. ► We base our discussion on the use of the Weyl eigendifferentials. ► We give a generalized Lewis and Riesenfeld phase for continuous spectra. ► This generalized phase or Aharonov–Anandan geometric phase is linked to the S matrix. ► The modified Pöschl–Teller and the linear potential are worked out as illustrations. |
| doi_str_mv | 10.1016/j.physleta.2012.02.054 |
| format | Article |
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► In this Letter we study the exact quantum evolution for continuous spectra problems. ► We base our discussion on the use of the Weyl eigendifferentials. ► We give a generalized Lewis and Riesenfeld phase for continuous spectra. ► This generalized phase or Aharonov–Anandan geometric phase is linked to the S matrix. ► The modified Pöschl–Teller and the linear potential are worked out as illustrations.</description><identifier>ISSN: 0375-9601</identifier><identifier>EISSN: 1873-2429</identifier><identifier>DOI: 10.1016/j.physleta.2012.02.054</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Continuous spectrum ; Derivation ; Evolution ; Geometrical phase ; Illustrations ; Invariants ; Lewis and Riesenfeld theory ; Non-adiabatic evolution ; Quantum mechanics ; Quantum theory ; Scattering matrix ; Solid state physics ; Subspaces</subject><ispartof>Physics letters. A, 2012-03, Vol.376 (16), p.1328-1334</ispartof><rights>2012 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c345t-2694e6acd4bbc7978362f7c75d896e60cbe55ae44578a76640c7ae2c8cd73c2b3</citedby><cites>FETCH-LOGICAL-c345t-2694e6acd4bbc7978362f7c75d896e60cbe55ae44578a76640c7ae2c8cd73c2b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0375960112002496$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids></links><search><creatorcontrib>Saadi, Y.</creatorcontrib><creatorcontrib>Maamache, M.</creatorcontrib><title>Non-adiabatic quantum evolution: The S matrix as a geometrical phase factor</title><title>Physics letters. A</title><description>We present a complete derivation of the exact evolution of quantum mechanics for the case when the underlying spectrum is continuous. We base our discussion on the use of the Weyl eigendifferentials. We show that a quantum system being in an eigenstate of an invariant will remain in the subspace generated by the eigenstates of the invariant, thereby acquiring a generalized non-adiabatic or Aharonov–Anandan geometric phase linked to the diagonal element of the S matrix. The modified Pöschl–Teller potential and the time-dependent linear potential are worked out as illustrations.
► In this Letter we study the exact quantum evolution for continuous spectra problems. ► We base our discussion on the use of the Weyl eigendifferentials. ► We give a generalized Lewis and Riesenfeld phase for continuous spectra. ► This generalized phase or Aharonov–Anandan geometric phase is linked to the S matrix. ► The modified Pöschl–Teller and the linear potential are worked out as illustrations.</description><subject>Continuous spectrum</subject><subject>Derivation</subject><subject>Evolution</subject><subject>Geometrical phase</subject><subject>Illustrations</subject><subject>Invariants</subject><subject>Lewis and Riesenfeld theory</subject><subject>Non-adiabatic evolution</subject><subject>Quantum mechanics</subject><subject>Quantum theory</subject><subject>Scattering matrix</subject><subject>Solid state physics</subject><subject>Subspaces</subject><issn>0375-9601</issn><issn>1873-2429</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNqFkE9r3DAQxUVoINukXyHo2Is3sqw_dk8toUlDl-aQ5CzG49msFttyJHlJvn0dtj0HHjwGfu_BPMYuS7EuRWmu9utp95Z6yrCWopRrsUirE7Yqa1sVUsnmE1uJyuqiMaI8Y59T2guxJEWzYr__hLGAzkML2SN_mWHM88DpEPo5-zB-44874g98gBz9K4fEgT9TGGg5EXo-7SAR3wLmEC_Y6Rb6RF_--Tl7uvn5eP2r2Nzf3l3_2BRYKZ0LaRpFBrBTbYu2sXVl5Nai1V3dGDICW9IaSClta7DGKIEWSGKNna1QttU5-3rsnWJ4mSllN_iE1PcwUpiTK4WUdSOErhbUHFGMIaVIWzdFP0B8WyD3vp7bu__ruff1nFik1RL8fgzS8sjBU3QJPY1InY-E2XXBf1TxFxqGfFs</recordid><startdate>20120319</startdate><enddate>20120319</enddate><creator>Saadi, Y.</creator><creator>Maamache, M.</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7QQ</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JG9</scope><scope>L7M</scope></search><sort><creationdate>20120319</creationdate><title>Non-adiabatic quantum evolution: The S matrix as a geometrical phase factor</title><author>Saadi, Y. ; Maamache, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c345t-2694e6acd4bbc7978362f7c75d896e60cbe55ae44578a76640c7ae2c8cd73c2b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Continuous spectrum</topic><topic>Derivation</topic><topic>Evolution</topic><topic>Geometrical phase</topic><topic>Illustrations</topic><topic>Invariants</topic><topic>Lewis and Riesenfeld theory</topic><topic>Non-adiabatic evolution</topic><topic>Quantum mechanics</topic><topic>Quantum theory</topic><topic>Scattering matrix</topic><topic>Solid state physics</topic><topic>Subspaces</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Saadi, Y.</creatorcontrib><creatorcontrib>Maamache, M.</creatorcontrib><collection>CrossRef</collection><collection>Ceramic Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Materials Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Physics letters. A</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Saadi, Y.</au><au>Maamache, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Non-adiabatic quantum evolution: The S matrix as a geometrical phase factor</atitle><jtitle>Physics letters. A</jtitle><date>2012-03-19</date><risdate>2012</risdate><volume>376</volume><issue>16</issue><spage>1328</spage><epage>1334</epage><pages>1328-1334</pages><issn>0375-9601</issn><eissn>1873-2429</eissn><abstract>We present a complete derivation of the exact evolution of quantum mechanics for the case when the underlying spectrum is continuous. We base our discussion on the use of the Weyl eigendifferentials. We show that a quantum system being in an eigenstate of an invariant will remain in the subspace generated by the eigenstates of the invariant, thereby acquiring a generalized non-adiabatic or Aharonov–Anandan geometric phase linked to the diagonal element of the S matrix. The modified Pöschl–Teller potential and the time-dependent linear potential are worked out as illustrations.
► In this Letter we study the exact quantum evolution for continuous spectra problems. ► We base our discussion on the use of the Weyl eigendifferentials. ► We give a generalized Lewis and Riesenfeld phase for continuous spectra. ► This generalized phase or Aharonov–Anandan geometric phase is linked to the S matrix. ► The modified Pöschl–Teller and the linear potential are worked out as illustrations.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.physleta.2012.02.054</doi><tpages>7</tpages></addata></record> |
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| source | Elsevier ScienceDirect Journals |
| subjects | Continuous spectrum Derivation Evolution Geometrical phase Illustrations Invariants Lewis and Riesenfeld theory Non-adiabatic evolution Quantum mechanics Quantum theory Scattering matrix Solid state physics Subspaces |
| title | Non-adiabatic quantum evolution: The S matrix as a geometrical phase factor |
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