The use of Laplace transform in the inverse problem from bound states

IF 2.1 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Romanian Reports in Physics Pub Date : 2023-09-15 DOI:10.59277/romrepphys.2023.75.114
R. MEZHOUD, I. AMI, R. J. LOMBARD
{"title":"The use of Laplace transform in the inverse problem from bound states","authors":"R. MEZHOUD, I. AMI, R. J. LOMBARD","doi":"10.59277/romrepphys.2023.75.114","DOIUrl":null,"url":null,"abstract":"\"In a previous work dedicated to non-relativistic quantum mechanics in the three-dimensional space with spherical symmetry, we have shown the possibility of reconstructing the ground state density from its moments in the case of bound states. The method is based on relationships connecting these moments to the lower energy of each state of angular momentum `. The ground state density yields the ground state wave function, which allows us to calculate the equivalent local potential by inverting the Schrodinger equation. This calculus uses the Fourier transform of the ground state density ρ(r). The aim of this work is to check how to improve the results by replacing the Fourier transform by the Laplace transform of the quantity r2 ρ(r). The method is first presented. Then examples and results are compared to those obtained previously. \"","PeriodicalId":49588,"journal":{"name":"Romanian Reports in Physics","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Romanian Reports in Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.59277/romrepphys.2023.75.114","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

"In a previous work dedicated to non-relativistic quantum mechanics in the three-dimensional space with spherical symmetry, we have shown the possibility of reconstructing the ground state density from its moments in the case of bound states. The method is based on relationships connecting these moments to the lower energy of each state of angular momentum `. The ground state density yields the ground state wave function, which allows us to calculate the equivalent local potential by inverting the Schrodinger equation. This calculus uses the Fourier transform of the ground state density ρ(r). The aim of this work is to check how to improve the results by replacing the Fourier transform by the Laplace transform of the quantity r2 ρ(r). The method is first presented. Then examples and results are compared to those obtained previously. "
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
拉普拉斯变换在束缚态反问题中的应用
“在之前的一项研究球面对称三维空间中的非相对论量子力学的工作中,我们已经展示了从束缚态的矩重建基态密度的可能性。该方法基于将这些力矩与角动量的每个状态的较低能量联系起来的关系。基态密度产生基态波函数,它允许我们通过反演薛定谔方程来计算等效的局域势。这个微积分使用了基态密度ρ(r)的傅里叶变换。这项工作的目的是检查如何通过用r2 ρ(r)的拉普拉斯变换代替傅里叶变换来改进结果。本文首次提出了该方法。然后将实例和结果与之前的结果进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Romanian Reports in Physics
Romanian Reports in Physics 物理-物理:综合
CiteScore
4.20
自引率
29.60%
发文量
0
审稿时长
4-8 weeks
期刊介绍: Romanian Reports in Physics is a journal publishing physics contributions in the fields of: 1. Mathematical and General Physics 2. Nuclear Physics. Particle Physics. Astroparticle Physics 3. Atomic and Molecular Physics 4. Plasma Physics 5. Condensed Matter 6. Optics & Quantum Electronics 7. Biophysics & Medical Physics. Environmental Physics 8. Physical Methods and Instrumentation 9. Earth Physics
期刊最新文献
Investigation of the magnetic field created by axially symmetric permanent magnet arrangements Indoor air quality monitoring in educational environments: a case study Painlevé integrability for an extended (3 + 1)-dimensional Bogoyavlensky-Konopelchenko equation: lumps and multiple soliton solutions Computational characterization of coaxial HPGe detectors using Monte Carlo simulation and nonlinear least squares optimization Lump and multiple soliton solutions to the new integrable (3+1)-dimensional Boussinesq equation
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1