{"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":null,"pages":null},"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}
引用次数: 0
Abstract
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.
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).