相对论单粒子态的计算

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

Few-Body Systems Pub Date : 2023-11-13 DOI:10.1007/s00601-023-01869-y

D. Wingard, B. Kónya, Z. Papp

{"title":"相对论单粒子态的计算","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":"{\"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}","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

摘要

提出了一种计算束缚态和共振态的方法，分别通过求解实能量的Klein-Gordon方程和复能量的Dirac方程来计算。该方法是一种非相对论性方法的扩展，其中势用库仑-斯图尔曼基表示。这一基础有助于用连分式对库仑格林算子进行精确的解析计算。在对相对论问题的推广中，我们将Klein-Gordon和Dirac方程转化为有效的Schrödinger形式。那么解的方法基本上是将非相对论量如角动量、电荷、能量和势解析延拓为有效的相对论对应量。

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

Calculation of Relativistic Single-Particle States

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.

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).