{"title":"Quantum Harmonic Oscillator in a Time Dependent Noncommutative Background","authors":"Manjari Dutta, Shreemoyee Ganguly, Sunandan Gangopadhyay","doi":"10.1007/s10773-024-05707-7","DOIUrl":null,"url":null,"abstract":"<p>This work explores the behaviour of a noncommutative harmonic oscillator in a time-dependent background, as previously investigated in Dey and Fring (Phys. Rev. D <b>90</b>, 084005, 2014). Specifically, we examine the system when expressed in terms of commutative variables, utilizing a generalized form of the standard Bopp-shift relations recently introduced in Biswas et al. (Phys. Rev. A <b>102</b>, 022231, 2020). We solved the time dependent system and obtained the analytical form of the eigenfunction using the method of Lewis invariants, which is associated with the Ermakov-Pinney equation, a non-linear differential equation. We then obtain exact analytical solution set for the Ermakov-Pinney equation. With these solutions in place, we move on to compute the dynamics of the energy expectation value analytically and explore their graphical representations for various solution sets of the Ermakov-Pinney equation, associated with a particular choice of quantum number. Finally, we determined the generalized form of the uncertainty equality relations among the operators for both commutative and noncommutative cases. Expectedly, our study is consistent with the findings in Dey and Fring (Phys. Rev. D <b>90</b>, 084005, 2014), specifically in a particular limit where the coordinate mapping relations reduce to the standard Bopp-shift relations.</p>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-07-09","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/s10773-024-05707-7","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}
引用次数: 0
Abstract
This work explores the behaviour of a noncommutative harmonic oscillator in a time-dependent background, as previously investigated in Dey and Fring (Phys. Rev. D 90, 084005, 2014). Specifically, we examine the system when expressed in terms of commutative variables, utilizing a generalized form of the standard Bopp-shift relations recently introduced in Biswas et al. (Phys. Rev. A 102, 022231, 2020). We solved the time dependent system and obtained the analytical form of the eigenfunction using the method of Lewis invariants, which is associated with the Ermakov-Pinney equation, a non-linear differential equation. We then obtain exact analytical solution set for the Ermakov-Pinney equation. With these solutions in place, we move on to compute the dynamics of the energy expectation value analytically and explore their graphical representations for various solution sets of the Ermakov-Pinney equation, associated with a particular choice of quantum number. Finally, we determined the generalized form of the uncertainty equality relations among the operators for both commutative and noncommutative cases. Expectedly, our study is consistent with the findings in Dey and Fring (Phys. Rev. D 90, 084005, 2014), specifically in a particular limit where the coordinate mapping relations reduce to the standard Bopp-shift relations.
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.