Numerical approach by quasi-spectral and fitting methods to study Schrodinger equation and calculating the energy levels of flat potentials

Q4 Physics and Astronomy
{"title":"Numerical approach by quasi-spectral and fitting methods to study Schrodinger equation and calculating the energy levels of flat potentials","authors":"","doi":"10.47176/ijpr.22.4.91310","DOIUrl":null,"url":null,"abstract":"In this paper, flat potentials (μ│x / a│N) are numerically investigated by pseudo-spectral method. The Schrodinger equation of this type of potential has become an eigen system using the pseudo-spectral method. The eigen system is then diagonalized by the Jacobi method. Energy eigen values for different Ns have been compared with similar articles. The limit behavior of this potential for the states N = 2 and N → ∞ is related to the harmonic oscillator and the particle in the box with length 2a, respectively. For each N, a function is proposed for energy eigen values in terms of the quantum number n. By using of data fitting, the correctness of the proposed equation is checked.","PeriodicalId":38961,"journal":{"name":"Iranian Journal of Physics Research","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Iranian Journal of Physics Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47176/ijpr.22.4.91310","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0

Abstract

In this paper, flat potentials (μ│x / a│N) are numerically investigated by pseudo-spectral method. The Schrodinger equation of this type of potential has become an eigen system using the pseudo-spectral method. The eigen system is then diagonalized by the Jacobi method. Energy eigen values for different Ns have been compared with similar articles. The limit behavior of this potential for the states N = 2 and N → ∞ is related to the harmonic oscillator and the particle in the box with length 2a, respectively. For each N, a function is proposed for energy eigen values in terms of the quantum number n. By using of data fitting, the correctness of the proposed equation is checked.
数值方法采用拟谱法和拟合法研究薛定谔方程,计算平面势的能级
本文用伪谱法对平面电位(μ│x / a│N)进行了数值研究。这类势的薛定谔方程利用伪谱方法得到了一个本征系统。然后用雅可比方法对角化特征系统。不同Ns的能量特征值已与同类文章进行了比较。在N = 2和N→∞状态下,该势的极限行为分别与谐振子和长度为2a的盒子中的粒子有关。对于每一个N,提出了一个以量子数N表示的能量特征值的函数。通过数据拟合,检验了所提方程的正确性。
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 求助全文
来源期刊
Iranian Journal of Physics Research
Iranian Journal of Physics Research Physics and Astronomy-Physics and Astronomy (all)
CiteScore
0.20
自引率
0.00%
发文量
0
审稿时长
30 weeks
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信