特殊四体可解模型的代数方法

IF 1.7 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Few-Body Systems Pub Date : 2024-09-20 DOI:10.1007/s00601-024-01958-6

Z. Bakhshi, S. Khoshdooni, H. Rahmati

{"title":"特殊四体可解模型的代数方法","authors":"Z. Bakhshi, S. Khoshdooni, H. Rahmati","doi":"10.1007/s00601-024-01958-6","DOIUrl":null,"url":null,"abstract":"<div><p>A special four-body quantum model in one dimension with a discrete spectrum was introduced, including harmonic oscillator and three-body interaction potentials. After reducing one degree of freedom by using the Jacobian transformation in the center of mass, the desired Hamiltonian is examined in spherical coordinate with three degrees of freedom. To investigate this model algebraically, using the gauge rotation with the ground state wave function, the relation between the Hamiltonian and the generators of <span>\\(sl(3, {\\mathbb {R}})\\)</span> and <span>\\(sl(2, {\\mathbb {R}})\\)</span> Lie algebras is examined. Finally, this algebraic form helps us to get the Hamiltonian eigenvalues.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":"65 4","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algebraic Approach to a Special Four-Body Solvable Model\",\"authors\":\"Z. Bakhshi, S. Khoshdooni, H. Rahmati\",\"doi\":\"10.1007/s00601-024-01958-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A special four-body quantum model in one dimension with a discrete spectrum was introduced, including harmonic oscillator and three-body interaction potentials. After reducing one degree of freedom by using the Jacobian transformation in the center of mass, the desired Hamiltonian is examined in spherical coordinate with three degrees of freedom. To investigate this model algebraically, using the gauge rotation with the ground state wave function, the relation between the Hamiltonian and the generators of <span>\\\\(sl(3, {\\\\mathbb {R}})\\\\)</span> and <span>\\\\(sl(2, {\\\\mathbb {R}})\\\\)</span> Lie algebras is examined. Finally, this algebraic form helps us to get the Hamiltonian eigenvalues.</p></div>\",\"PeriodicalId\":556,\"journal\":{\"name\":\"Few-Body Systems\",\"volume\":\"65 4\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-09-20\",\"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/s00601-024-01958-6\",\"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/s00601-024-01958-6","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}

引用次数: 0

摘要

介绍了一维离散谱的特殊四体量子模型，包括谐振子和三体相互作用势。通过使用质量中心的雅各布变换减少一个自由度后，在球面坐标中用三个自由度检验了所需的哈密顿。为了从代数上研究这个模型，利用基态波函数的量规旋转，研究了哈密顿和 \(sl(3, {\mathbb {R}})\) 和 \(sl(2, {\mathbb {R}})\) 的生成器之间的关系。李代数进行了研究。最后，这种代数形式有助于我们得到哈密顿特征值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Algebraic Approach to a Special Four-Body Solvable Model

A special four-body quantum model in one dimension with a discrete spectrum was introduced, including harmonic oscillator and three-body interaction potentials. After reducing one degree of freedom by using the Jacobian transformation in the center of mass, the desired Hamiltonian is examined in spherical coordinate with three degrees of freedom. To investigate this model algebraically, using the gauge rotation with the ground state wave function, the relation between the Hamiltonian and the generators of \(sl(3, {\mathbb {R}})\) and \(sl(2, {\mathbb {R}})\) Lie algebras is examined. Finally, this algebraic form helps us to get the Hamiltonian eigenvalues.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Few-Body Systems 物理-物理：综合

CiteScore

2.90

自引率

18.80%

发文量

审稿时长

6-12 weeks

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).