{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T14:07:01Z","timestamp":1772287621203,"version":"3.50.1"},"reference-count":21,"publisher":"IOP Publishing","issue":"9","license":[{"start":{"date-parts":[[2019,7,10]],"date-time":"2019-07-10T00:00:00Z","timestamp":1562716800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2019,7,10]],"date-time":"2019-07-10T00:00:00Z","timestamp":1562716800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"1Portuguese Government through the FCT - Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["PEst-C\/MAT\/UI0324\/2011"],"award-info":[{"award-number":["PEst-C\/MAT\/UI0324\/2011"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Phys. Scr."],"published-print":{"date-parts":[[2019,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Non-self-adjoint operators with a real discrete spectrum exhibit, in general, a quite different behavior from the one of self-adjoint operators, with the same spectrum. This fact has serious mathematical and physical implications, namely in the rigorous formulation of quantum mechanics (QM), where self-adjointness plays a central role, in particular in the spectral analysis of the involved operators. In this framework, a non-self-adjoint 2D-harmonic oscillator is considered. Its eigenvalues and eigenfunctions, as well as those of its adjoint, are explicitly determined. Although the eigensystems are complete they may not form bases, a drawback for the mathematical formulation of the QM of the system. The existence of a metric operator defining an inner product which renders the Hamiltonian self-adjoint, is discussed.<\/jats:p>","DOI":"10.1088\/1402-4896\/ab1bf0","type":"journal-article","created":{"date-parts":[[2019,4,24]],"date-time":"2019-04-24T18:19:03Z","timestamp":1556129943000},"page":"095205","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["A quantum system with a non-self-adjoint 2D-harmonic oscillator"],"prefix":"10.1088","volume":"94","author":[{"given":"N","family":"Bebiano","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2614-7775","authenticated-orcid":false,"given":"J","family":"da Provid\u00eancia","sequence":"additional","affiliation":[]},{"given":"J P da","family":"Provid\u00eancia","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2019,7,10]]},"reference":[{"key":"psab1bf0bib1","author":"Davidov","year":"1965","type":"book"},{"key":"psab1bf0bib2","doi-asserted-by":"publisher","first-page":"969","DOI":"10.1007\/s10955-007-9321-1","type":"journal-article","article-title":"Hamiltonian structure for dispersive and dissipative dynamical systems","volume":"128","author":"Figotin","year":"2007","journal-title":"J. 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All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2019-02-25","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2019-04-24","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2019-07-10","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}