{"title":"最小长度不确定性关系内的矢量平面 DKP 振荡器","authors":"Amenallah Andolsi, Yassine Chargui, Adel Trabelsi","doi":"10.1007/s00601-024-01884-7","DOIUrl":null,"url":null,"abstract":"<div><p>In this work, we investigate the solutions of the two-dimensional Duffin–Kemmer–Petiau oscillator for spin-one particles under a minimal length assumption. To incorporate the minimal length, we assume a generalized uncertainty principle with two deformation parameters implying a noncommutative phase space. By employing the momentum representation, we were able to solve the problem exactly for all spin projection numbers and obtain the minimal length corrections brought to the energy eigenvalues and the associated eigenstates of the oscillator. The solutions are systematically classified into natural and unnatural parity states contingent upon the spin-projection numbers. Additionally, we studied the effect of applying an external transverse homogeneous magnetic field (HMF) on the dynamics of the system. In particular, the motion of a spin-one boson moving in the plane under a HMF is considered as a special case. We also discuss the nonrelativistic limit of the energy eigenvalues in each one of the considered instances.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"65 2","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Vector Planar DKP Oscillator Within a Minimal Length Uncertainty Relation\",\"authors\":\"Amenallah Andolsi, Yassine Chargui, Adel Trabelsi\",\"doi\":\"10.1007/s00601-024-01884-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this work, we investigate the solutions of the two-dimensional Duffin–Kemmer–Petiau oscillator for spin-one particles under a minimal length assumption. To incorporate the minimal length, we assume a generalized uncertainty principle with two deformation parameters implying a noncommutative phase space. By employing the momentum representation, we were able to solve the problem exactly for all spin projection numbers and obtain the minimal length corrections brought to the energy eigenvalues and the associated eigenstates of the oscillator. The solutions are systematically classified into natural and unnatural parity states contingent upon the spin-projection numbers. Additionally, we studied the effect of applying an external transverse homogeneous magnetic field (HMF) on the dynamics of the system. In particular, the motion of a spin-one boson moving in the plane under a HMF is considered as a special case. We also discuss the nonrelativistic limit of the energy eigenvalues in each one of the considered instances.</p></div>\",\"PeriodicalId\":556,\"journal\":{\"name\":\"Few-Body Systems\",\"volume\":\"65 2\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-03-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Few-Body Systems\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00601-024-01884-7\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Few-Body Systems","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s00601-024-01884-7","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
The Vector Planar DKP Oscillator Within a Minimal Length Uncertainty Relation
In this work, we investigate the solutions of the two-dimensional Duffin–Kemmer–Petiau oscillator for spin-one particles under a minimal length assumption. To incorporate the minimal length, we assume a generalized uncertainty principle with two deformation parameters implying a noncommutative phase space. By employing the momentum representation, we were able to solve the problem exactly for all spin projection numbers and obtain the minimal length corrections brought to the energy eigenvalues and the associated eigenstates of the oscillator. The solutions are systematically classified into natural and unnatural parity states contingent upon the spin-projection numbers. Additionally, we studied the effect of applying an external transverse homogeneous magnetic field (HMF) on the dynamics of the system. In particular, the motion of a spin-one boson moving in the plane under a HMF is considered as a special case. We also discuss the nonrelativistic limit of the energy eigenvalues in each one of the considered instances.
期刊介绍:
The journal Few-Body Systems presents original research work – experimental, theoretical and computational – investigating the behavior of any classical or quantum system consisting of a small number of well-defined constituent structures. The focus is on the research methods, properties, and results characteristic of few-body systems. Examples of few-body systems range from few-quark states, light nuclear and hadronic systems; few-electron atomic systems and small molecules; and specific systems in condensed matter and surface physics (such as quantum dots and highly correlated trapped systems), up to and including large-scale celestial structures.
Systems for which an equivalent one-body description is available or can be designed, and large systems for which specific many-body methods are needed are outside the scope of the journal.
The journal is devoted to the publication of all aspects of few-body systems research and applications. While concentrating on few-body systems well-suited to rigorous solutions, the journal also encourages interdisciplinary contributions that foster common approaches and insights, introduce and benchmark the use of novel tools (e.g. machine learning) and develop relevant applications (e.g. few-body aspects in quantum technologies).