{"title":"动态非交换空间中的克莱因-戈登振荡器","authors":"Ilyas Haouam","doi":"10.1007/s10773-024-05696-7","DOIUrl":null,"url":null,"abstract":"<p>This paper aims to investigate the two-dimensional Klein-Gordon oscillator system in a dynamical noncommutative (DNC) space. We address the deformed system using the time-independent perturbation theory, where the energy eigenvalues and eigenvectors are obtained in relativistic and nonrelativistic regimes, also the effects of the dynamical and non-dynamical noncommutative settings are successfully examined. Then some numerical results are given and used to extensively study the conduct of the system under the various considerations. Note that in the DNC space, the space-space commutation relations and noncommutative parameter are position-dependent. The first-order corrections to the eigensystem are found, then, it is shown that the energy shift depends on the DNC parameter <span>\\(\\tau \\)</span>. Moreover, using the accuracy of energy measurement, we put an upper bound on the parameter <span>\\(\\tau \\)</span>. Knowing that, with a set of two-dimensional Bopp-shift transformation, we link the noncommutative problem to the standard commutative one.</p>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Klein-Gordon Oscillator In Dynamical Noncommutative Space\",\"authors\":\"Ilyas Haouam\",\"doi\":\"10.1007/s10773-024-05696-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper aims to investigate the two-dimensional Klein-Gordon oscillator system in a dynamical noncommutative (DNC) space. We address the deformed system using the time-independent perturbation theory, where the energy eigenvalues and eigenvectors are obtained in relativistic and nonrelativistic regimes, also the effects of the dynamical and non-dynamical noncommutative settings are successfully examined. Then some numerical results are given and used to extensively study the conduct of the system under the various considerations. Note that in the DNC space, the space-space commutation relations and noncommutative parameter are position-dependent. The first-order corrections to the eigensystem are found, then, it is shown that the energy shift depends on the DNC parameter <span>\\\\(\\\\tau \\\\)</span>. Moreover, using the accuracy of energy measurement, we put an upper bound on the parameter <span>\\\\(\\\\tau \\\\)</span>. Knowing that, with a set of two-dimensional Bopp-shift transformation, we link the noncommutative problem to the standard commutative one.</p>\",\"PeriodicalId\":597,\"journal\":{\"name\":\"International Journal of Theoretical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-07-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Theoretical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s10773-024-05696-7\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s10773-024-05696-7","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Klein-Gordon Oscillator In Dynamical Noncommutative Space
This paper aims to investigate the two-dimensional Klein-Gordon oscillator system in a dynamical noncommutative (DNC) space. We address the deformed system using the time-independent perturbation theory, where the energy eigenvalues and eigenvectors are obtained in relativistic and nonrelativistic regimes, also the effects of the dynamical and non-dynamical noncommutative settings are successfully examined. Then some numerical results are given and used to extensively study the conduct of the system under the various considerations. Note that in the DNC space, the space-space commutation relations and noncommutative parameter are position-dependent. The first-order corrections to the eigensystem are found, then, it is shown that the energy shift depends on the DNC parameter \(\tau \). Moreover, using the accuracy of energy measurement, we put an upper bound on the parameter \(\tau \). Knowing that, with a set of two-dimensional Bopp-shift transformation, we link the noncommutative problem to the standard commutative one.
期刊介绍:
International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.