{"title":"Calculation of Relativistic Single-Particle States","authors":"D. Wingard, B. Kónya, Z. Papp","doi":"10.1007/s00601-023-01869-y","DOIUrl":null,"url":null,"abstract":"<div><p>A computational method is proposed to calculate bound and resonant states by solving the Klein–Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential is represented in a Coulomb–Sturmian basis. This basis facilitates the exact analytic evaluation of the Coulomb Green’s operator in terms of a continued fraction. In the extension to relativistic problems, we cast the Klein–Gordon and Dirac equations into an effective Schrödinger form. Then the solution method is basically an analytic continuation of non-relativistic quantities like the angular momentum, charge, energy and potential into the effective relativistic counterparts.</p></div>","PeriodicalId":556,"journal":{"name":"Few-Body Systems","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2023-11-13","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/s00601-023-01869-y","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 computational method is proposed to calculate bound and resonant states by solving the Klein–Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential is represented in a Coulomb–Sturmian basis. This basis facilitates the exact analytic evaluation of the Coulomb Green’s operator in terms of a continued fraction. In the extension to relativistic problems, we cast the Klein–Gordon and Dirac equations into an effective Schrödinger form. Then the solution method is basically an analytic continuation of non-relativistic quantities like the angular momentum, charge, energy and potential into the effective relativistic counterparts.
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).
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