从标准到广义Schrödinger和Klein-Gordon方程：从属法

IF 3 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Annals of Physics Pub Date : 2025-04-21 DOI:10.1016/j.aop.2025.170034

Trifce Sandev , Irina Petreska , Alexander Iomin

{"title":"从标准到广义Schrödinger和Klein-Gordon方程：从属法","authors":"Trifce Sandev , Irina Petreska , Alexander Iomin","doi":"10.1016/j.aop.2025.170034","DOIUrl":null,"url":null,"abstract":"<div><div>We derive generalized versions of the Schrödinger and Klein–Gordon equations from the corresponding standard Schrödinger and Klein–Gordon equations by means of the subordination approach. A special cases of time fractional Schrödinger and Klein–Gordon equations are obtained for the Lévy <span><math><mi>α</mi></math></span>-stable subordinator. It has been shown that the Caputo time fractional derivatives in quantum mechanics (relativistic and non-relativistic) are due to the Lévy stable processes in time with a characteristic time scale <span><math><mi>τ</mi></math></span>, such that the fractional time is dimensionless according to the ratio <span><math><mrow><mi>t</mi><mo>/</mo><mi>τ</mi></mrow></math></span>.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"479 ","pages":"Article 170034"},"PeriodicalIF":3.0000,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"From standard to generalized Schrödinger and Klein–Gordon equations: Subordination approach\",\"authors\":\"Trifce Sandev , Irina Petreska , Alexander Iomin\",\"doi\":\"10.1016/j.aop.2025.170034\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We derive generalized versions of the Schrödinger and Klein–Gordon equations from the corresponding standard Schrödinger and Klein–Gordon equations by means of the subordination approach. A special cases of time fractional Schrödinger and Klein–Gordon equations are obtained for the Lévy <span><math><mi>α</mi></math></span>-stable subordinator. It has been shown that the Caputo time fractional derivatives in quantum mechanics (relativistic and non-relativistic) are due to the Lévy stable processes in time with a characteristic time scale <span><math><mi>τ</mi></math></span>, such that the fractional time is dimensionless according to the ratio <span><math><mrow><mi>t</mi><mo>/</mo><mi>τ</mi></mrow></math></span>.</div></div>\",\"PeriodicalId\":8249,\"journal\":{\"name\":\"Annals of Physics\",\"volume\":\"479 \",\"pages\":\"Article 170034\"},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2025-04-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0003491625001150\",\"RegionNum\":3,\"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":"Annals of Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0003491625001150","RegionNum":3,"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

利用从属法，从相应的标准方程Schrödinger和Klein-Gordon方程推导出Schrödinger和Klein-Gordon方程的广义版本。得到了lsamvy α-稳定从属系统的时间分数方程Schrödinger和Klein-Gordon方程的一个特例。已经证明，量子力学中的Caputo时间分数阶导数（相对论和非相对论）是由于具有特征时间尺度τ的l稳定过程，使得分数时间按照t/τ的比例是无因次的。

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

From standard to generalized Schrödinger and Klein–Gordon equations: Subordination approach

We derive generalized versions of the Schrödinger and Klein–Gordon equations from the corresponding standard Schrödinger and Klein–Gordon equations by means of the subordination approach. A special cases of time fractional Schrödinger and Klein–Gordon equations are obtained for the Lévy

α

-stable subordinator. It has been shown that the Caputo time fractional derivatives in quantum mechanics (relativistic and non-relativistic) are due to the Lévy stable processes in time with a characteristic time scale

τ

, such that the fractional time is dimensionless according to the ratio

t / τ

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

Annals of Physics 物理-物理：综合

CiteScore

5.30

自引率

3.30%

发文量

211

审稿时长

47 days

期刊介绍： Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance. The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.