Quantized-Energy Equation for N-Level Atom in the Probability Representation of Quantum Mechanics
For Hermitian and non-Hermitian Hamiltonian matrices H , we present the Schr ̈odinger equation for qudit (spin- j system, N -level atom) with the state vector | ψ 〉 in a new form of the linear eigenvalue equation for the matrix H = ( H ⊗ 1 N ) and the probability eigenvector | p 〉 identified with qu...
Gespeichert in:
| Veröffentlicht in: | Journal of Russian laser research 2020-11, Vol.41 (6), p.576-583 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 583 |
|---|---|
| container_issue | 6 |
| container_start_page | 576 |
| container_title | Journal of Russian laser research |
| container_volume | 41 |
| creator | Chernega, Vladimir N. Man’ko, Margarita A. Man’ko, Vladimir I. |
| description | For Hermitian and non-Hermitian Hamiltonian matrices
H
, we present the Schr ̈odinger equation for qudit (spin-
j
system,
N
-level atom) with the state vector |
ψ
〉 in a new form of the linear eigenvalue equation for the matrix
H
= (
H
⊗ 1
N
) and the probability eigenvector |
p
〉 identified with quantum states in the probability representation of quantum mechanics. We discuss the possibility to experimentally detect the difference between the system states described by the solutions, corresponding to the Schrödinger equation with Hermitian and non-Hermitian Hamiltonians, by measuring the probabilities of artificial spin-1
/
2 projections
m
= ± 1
/
2, sets of which are identified with qudit states. We show that different symmetries of systems, including PT -symmetry and broken PT -symmetry, are determined by a set of
N
complex eigenvalues of the Hamiltonian matrix
H
. |
| doi_str_mv | 10.1007/s10946-020-09912-7 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2473784535</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2473784535</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-6caf15fef85afd9153634ba99907d592e62a401401abfa105fb40764d660fe6a3</originalsourceid><addsrcrecordid>eNp9kE1LAzEQhoMoWKt_wFPAc3Sy2SSbYyn1A-oneg7Z3aTd0m7aJCvUX-_aFbwJAzOH93kHHoQuKVxTAHkTKahcEMiAgFI0I_IIjSiXjBRSwHF_g6QkK5g4RWcxrgBAFYUaIfPamTY1X7Yms9aGxR7Pdp1JjW-x8wE_kbn9tGs8SX6DmxanpcUvwZembNZN2uM3uw022jYNiHf40Ndt8KOtlqZtqniOTpxZR3vxu8fo43b2Pr0n8-e7h-lkTipGVSKiMo5yZ13BjasV5UywvDRKKZA1V5kVmcmB9mNKZyhwV-YgRV4LAc4Kw8boaujdBr_rbEx65bvQ9i91lksmi5wz3qeyIVUFH2OwTm9DszFhrynoH5V6UKl7lfqgUsseYgMU-3C7sOGv-h_qGwR7dxM</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2473784535</pqid></control><display><type>article</type><title>Quantized-Energy Equation for N-Level Atom in the Probability Representation of Quantum Mechanics</title><source>SpringerLink Journals - AutoHoldings</source><creator>Chernega, Vladimir N. ; Man’ko, Margarita A. ; Man’ko, Vladimir I.</creator><creatorcontrib>Chernega, Vladimir N. ; Man’ko, Margarita A. ; Man’ko, Vladimir I.</creatorcontrib><description>For Hermitian and non-Hermitian Hamiltonian matrices
H
, we present the Schr ̈odinger equation for qudit (spin-
j
system,
N
-level atom) with the state vector |
ψ
〉 in a new form of the linear eigenvalue equation for the matrix
H
= (
H
⊗ 1
N
) and the probability eigenvector |
p
〉 identified with quantum states in the probability representation of quantum mechanics. We discuss the possibility to experimentally detect the difference between the system states described by the solutions, corresponding to the Schrödinger equation with Hermitian and non-Hermitian Hamiltonians, by measuring the probabilities of artificial spin-1
/
2 projections
m
= ± 1
/
2, sets of which are identified with qudit states. We show that different symmetries of systems, including PT -symmetry and broken PT -symmetry, are determined by a set of
N
complex eigenvalues of the Hamiltonian matrix
H
.</description><identifier>ISSN: 1071-2836</identifier><identifier>EISSN: 1573-8760</identifier><identifier>DOI: 10.1007/s10946-020-09912-7</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Eigenvalues ; Eigenvectors ; Hamiltonian functions ; Lasers ; Mathematical analysis ; Matrix methods ; Microwaves ; Optical Devices ; Optics ; Photonics ; Physics ; Physics and Astronomy ; Probability ; Quantum mechanics ; Quantum physics ; Representations ; RF and Optical Engineering ; Schrodinger equation ; State vectors ; Symmetry</subject><ispartof>Journal of Russian laser research, 2020-11, Vol.41 (6), p.576-583</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-6caf15fef85afd9153634ba99907d592e62a401401abfa105fb40764d660fe6a3</citedby><cites>FETCH-LOGICAL-c319t-6caf15fef85afd9153634ba99907d592e62a401401abfa105fb40764d660fe6a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10946-020-09912-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10946-020-09912-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Chernega, Vladimir N.</creatorcontrib><creatorcontrib>Man’ko, Margarita A.</creatorcontrib><creatorcontrib>Man’ko, Vladimir I.</creatorcontrib><title>Quantized-Energy Equation for N-Level Atom in the Probability Representation of Quantum Mechanics</title><title>Journal of Russian laser research</title><addtitle>J Russ Laser Res</addtitle><description>For Hermitian and non-Hermitian Hamiltonian matrices
H
, we present the Schr ̈odinger equation for qudit (spin-
j
system,
N
-level atom) with the state vector |
ψ
〉 in a new form of the linear eigenvalue equation for the matrix
H
= (
H
⊗ 1
N
) and the probability eigenvector |
p
〉 identified with quantum states in the probability representation of quantum mechanics. We discuss the possibility to experimentally detect the difference between the system states described by the solutions, corresponding to the Schrödinger equation with Hermitian and non-Hermitian Hamiltonians, by measuring the probabilities of artificial spin-1
/
2 projections
m
= ± 1
/
2, sets of which are identified with qudit states. We show that different symmetries of systems, including PT -symmetry and broken PT -symmetry, are determined by a set of
N
complex eigenvalues of the Hamiltonian matrix
H
.</description><subject>Eigenvalues</subject><subject>Eigenvectors</subject><subject>Hamiltonian functions</subject><subject>Lasers</subject><subject>Mathematical analysis</subject><subject>Matrix methods</subject><subject>Microwaves</subject><subject>Optical Devices</subject><subject>Optics</subject><subject>Photonics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Probability</subject><subject>Quantum mechanics</subject><subject>Quantum physics</subject><subject>Representations</subject><subject>RF and Optical Engineering</subject><subject>Schrodinger equation</subject><subject>State vectors</subject><subject>Symmetry</subject><issn>1071-2836</issn><issn>1573-8760</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKt_wFPAc3Sy2SSbYyn1A-oneg7Z3aTd0m7aJCvUX-_aFbwJAzOH93kHHoQuKVxTAHkTKahcEMiAgFI0I_IIjSiXjBRSwHF_g6QkK5g4RWcxrgBAFYUaIfPamTY1X7Yms9aGxR7Pdp1JjW-x8wE_kbn9tGs8SX6DmxanpcUvwZembNZN2uM3uw022jYNiHf40Ndt8KOtlqZtqniOTpxZR3vxu8fo43b2Pr0n8-e7h-lkTipGVSKiMo5yZ13BjasV5UywvDRKKZA1V5kVmcmB9mNKZyhwV-YgRV4LAc4Kw8boaujdBr_rbEx65bvQ9i91lksmi5wz3qeyIVUFH2OwTm9DszFhrynoH5V6UKl7lfqgUsseYgMU-3C7sOGv-h_qGwR7dxM</recordid><startdate>20201101</startdate><enddate>20201101</enddate><creator>Chernega, Vladimir N.</creator><creator>Man’ko, Margarita A.</creator><creator>Man’ko, Vladimir I.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20201101</creationdate><title>Quantized-Energy Equation for N-Level Atom in the Probability Representation of Quantum Mechanics</title><author>Chernega, Vladimir N. ; Man’ko, Margarita A. ; Man’ko, Vladimir I.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-6caf15fef85afd9153634ba99907d592e62a401401abfa105fb40764d660fe6a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Eigenvalues</topic><topic>Eigenvectors</topic><topic>Hamiltonian functions</topic><topic>Lasers</topic><topic>Mathematical analysis</topic><topic>Matrix methods</topic><topic>Microwaves</topic><topic>Optical Devices</topic><topic>Optics</topic><topic>Photonics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Probability</topic><topic>Quantum mechanics</topic><topic>Quantum physics</topic><topic>Representations</topic><topic>RF and Optical Engineering</topic><topic>Schrodinger equation</topic><topic>State vectors</topic><topic>Symmetry</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chernega, Vladimir N.</creatorcontrib><creatorcontrib>Man’ko, Margarita A.</creatorcontrib><creatorcontrib>Man’ko, Vladimir I.</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of Russian laser research</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chernega, Vladimir N.</au><au>Man’ko, Margarita A.</au><au>Man’ko, Vladimir I.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Quantized-Energy Equation for N-Level Atom in the Probability Representation of Quantum Mechanics</atitle><jtitle>Journal of Russian laser research</jtitle><stitle>J Russ Laser Res</stitle><date>2020-11-01</date><risdate>2020</risdate><volume>41</volume><issue>6</issue><spage>576</spage><epage>583</epage><pages>576-583</pages><issn>1071-2836</issn><eissn>1573-8760</eissn><abstract>For Hermitian and non-Hermitian Hamiltonian matrices
H
, we present the Schr ̈odinger equation for qudit (spin-
j
system,
N
-level atom) with the state vector |
ψ
〉 in a new form of the linear eigenvalue equation for the matrix
H
= (
H
⊗ 1
N
) and the probability eigenvector |
p
〉 identified with quantum states in the probability representation of quantum mechanics. We discuss the possibility to experimentally detect the difference between the system states described by the solutions, corresponding to the Schrödinger equation with Hermitian and non-Hermitian Hamiltonians, by measuring the probabilities of artificial spin-1
/
2 projections
m
= ± 1
/
2, sets of which are identified with qudit states. We show that different symmetries of systems, including PT -symmetry and broken PT -symmetry, are determined by a set of
N
complex eigenvalues of the Hamiltonian matrix
H
.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10946-020-09912-7</doi><tpages>8</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1071-2836 |
| ispartof | Journal of Russian laser research, 2020-11, Vol.41 (6), p.576-583 |
| issn | 1071-2836 1573-8760 |
| language | eng |
| recordid | cdi_proquest_journals_2473784535 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Eigenvalues Eigenvectors Hamiltonian functions Lasers Mathematical analysis Matrix methods Microwaves Optical Devices Optics Photonics Physics Physics and Astronomy Probability Quantum mechanics Quantum physics Representations RF and Optical Engineering Schrodinger equation State vectors Symmetry |
| title | Quantized-Energy Equation for N-Level Atom in the Probability Representation of Quantum Mechanics |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-03T23%3A58%3A13IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Quantized-Energy%20Equation%20for%20N-Level%20Atom%20in%20the%20Probability%20Representation%20of%20Quantum%20Mechanics&rft.jtitle=Journal%20of%20Russian%20laser%20research&rft.au=Chernega,%20Vladimir%20N.&rft.date=2020-11-01&rft.volume=41&rft.issue=6&rft.spage=576&rft.epage=583&rft.pages=576-583&rft.issn=1071-2836&rft.eissn=1573-8760&rft_id=info:doi/10.1007/s10946-020-09912-7&rft_dat=%3Cproquest_cross%3E2473784535%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2473784535&rft_id=info:pmid/&rfr_iscdi=true |