Non-Hermitian noncommutative quantum mechanics
. In this work we present a general formalism to treat non-Hermitian and noncommutative Hamiltonians. This is done employing the phase-space formalism of quantum mechanics, which allows to write a set of robust maps connecting the Hamitonians and the associated Wigner functions to the different Hilb...
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| Veröffentlicht in: | European physical journal plus 2019-07, Vol.134 (7), p.332, Article 332 |
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| creator | dos Santos, J. F. G. Luiz, F. S. Duarte, O. S. Moussa, M. H. Y. |
| description | .
In this work we present a general formalism to treat non-Hermitian and noncommutative Hamiltonians. This is done employing the phase-space formalism of quantum mechanics, which allows to write a set of robust maps connecting the Hamitonians and the associated Wigner functions to the different Hilbert space structures, namely, those describing the non-Hermitian and noncommutative, Hermitian and noncommutative, and Hermitian and commutative systems. A general recipe is provided to obtain the expected values of the more general Hamiltonian. Finally, we apply our method to the harmonic oscillator under linear amplification and discuss the implications of both non-Hermitian and noncommutative effects. |
| doi_str_mv | 10.1140/epjp/i2019-12738-3 |
| format | Article |
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In this work we present a general formalism to treat non-Hermitian and noncommutative Hamiltonians. This is done employing the phase-space formalism of quantum mechanics, which allows to write a set of robust maps connecting the Hamitonians and the associated Wigner functions to the different Hilbert space structures, namely, those describing the non-Hermitian and noncommutative, Hermitian and noncommutative, and Hermitian and commutative systems. A general recipe is provided to obtain the expected values of the more general Hamiltonian. Finally, we apply our method to the harmonic oscillator under linear amplification and discuss the implications of both non-Hermitian and noncommutative effects.</description><identifier>ISSN: 2190-5444</identifier><identifier>EISSN: 2190-5444</identifier><identifier>DOI: 10.1140/epjp/i2019-12738-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied and Technical Physics ; Atomic ; Complex Systems ; Condensed Matter Physics ; Eigenvalues ; Expected values ; Formalism ; Hamiltonian functions ; Harmonic oscillators ; Hilbert space ; Mathematical and Computational Physics ; Molecular ; Optical and Plasma Physics ; Physics ; Physics and Astronomy ; Quantum mechanics ; Quantum physics ; Regular Article ; Theoretical</subject><ispartof>European physical journal plus, 2019-07, Vol.134 (7), p.332, Article 332</ispartof><rights>Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019</rights><rights>Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-e1b05b298ffabb7ce4cbff6253307acb0627770d235e359248e869d1674e24d63</citedby><cites>FETCH-LOGICAL-c319t-e1b05b298ffabb7ce4cbff6253307acb0627770d235e359248e869d1674e24d63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1140/epjp/i2019-12738-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2919926197?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,776,780,21367,27901,27902,33721,41464,42533,43781,51294</link.rule.ids></links><search><creatorcontrib>dos Santos, J. F. G.</creatorcontrib><creatorcontrib>Luiz, F. S.</creatorcontrib><creatorcontrib>Duarte, O. S.</creatorcontrib><creatorcontrib>Moussa, M. H. Y.</creatorcontrib><title>Non-Hermitian noncommutative quantum mechanics</title><title>European physical journal plus</title><addtitle>Eur. Phys. J. Plus</addtitle><description>.
In this work we present a general formalism to treat non-Hermitian and noncommutative Hamiltonians. This is done employing the phase-space formalism of quantum mechanics, which allows to write a set of robust maps connecting the Hamitonians and the associated Wigner functions to the different Hilbert space structures, namely, those describing the non-Hermitian and noncommutative, Hermitian and noncommutative, and Hermitian and commutative systems. A general recipe is provided to obtain the expected values of the more general Hamiltonian. Finally, we apply our method to the harmonic oscillator under linear amplification and discuss the implications of both non-Hermitian and noncommutative effects.</description><subject>Applied and Technical Physics</subject><subject>Atomic</subject><subject>Complex Systems</subject><subject>Condensed Matter Physics</subject><subject>Eigenvalues</subject><subject>Expected values</subject><subject>Formalism</subject><subject>Hamiltonian functions</subject><subject>Harmonic oscillators</subject><subject>Hilbert space</subject><subject>Mathematical and Computational Physics</subject><subject>Molecular</subject><subject>Optical and Plasma Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum mechanics</subject><subject>Quantum physics</subject><subject>Regular Article</subject><subject>Theoretical</subject><issn>2190-5444</issn><issn>2190-5444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp9kMFKxDAQhoMouKz7Ap4KnrObSdKmOcqirrDoRc8hTafaYtNu0gq-vd2toCfnMnP4_n_gI-Qa2BpAsg32Tb-pOQNNgSuRU3FGFhw0o6mU8vzPfUlWMTZsGqlBarkg66fO0x2Gth5q6xPfede17TjYof7E5DBaP4xt0qJ7t7528YpcVPYj4upnL8nr_d3Ldkf3zw-P29s9dQL0QBEKlhZc51Vli0I5lK6oqoynQjBlXcEyrpRiJRcpilRzmWOe6RIyJZHLMhNLcjP39qE7jBgH03Rj8NNLwzVozTPQaqL4TLnQxRiwMn2oWxu-DDBzVGOOasxJjTmpMWIKiTkUJ9i_Yfit_if1DeJ1Z-Q</recordid><startdate>20190701</startdate><enddate>20190701</enddate><creator>dos Santos, J. 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In this work we present a general formalism to treat non-Hermitian and noncommutative Hamiltonians. This is done employing the phase-space formalism of quantum mechanics, which allows to write a set of robust maps connecting the Hamitonians and the associated Wigner functions to the different Hilbert space structures, namely, those describing the non-Hermitian and noncommutative, Hermitian and noncommutative, and Hermitian and commutative systems. A general recipe is provided to obtain the expected values of the more general Hamiltonian. Finally, we apply our method to the harmonic oscillator under linear amplification and discuss the implications of both non-Hermitian and noncommutative effects.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1140/epjp/i2019-12738-3</doi></addata></record> |
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| subjects | Applied and Technical Physics Atomic Complex Systems Condensed Matter Physics Eigenvalues Expected values Formalism Hamiltonian functions Harmonic oscillators Hilbert space Mathematical and Computational Physics Molecular Optical and Plasma Physics Physics Physics and Astronomy Quantum mechanics Quantum physics Regular Article Theoretical |
| title | Non-Hermitian noncommutative quantum mechanics |
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