The weakly bound states in Gaussian wells: From the binding energy of deuteron to the electronic structure of quantum dots

IF 2.3 3区 化学 Q3 CHEMISTRY, PHYSICAL International Journal of Quantum Chemistry Pub Date : 2024-07-31 DOI:10.1002/qua.27458
G. Rodriguez-Espejo, D. J. Nader, J. A. Segura-Landa, J. Ortiz-Monfil
{"title":"The weakly bound states in Gaussian wells: From the binding energy of deuteron to the electronic structure of quantum dots","authors":"G. Rodriguez-Espejo,&nbsp;D. J. Nader,&nbsp;J. A. Segura-Landa,&nbsp;J. Ortiz-Monfil","doi":"10.1002/qua.27458","DOIUrl":null,"url":null,"abstract":"<p>Gaussian potentials serve as a valuable tool for the comprehensive modeling of short-range interactions, spanning applications from Nuclear Physics to the artificial confinement of electrons within quantum dots. This study focuses on examining the lowest states within Gaussian wells, with particular emphasis on the weakly bound regime. The analysis delves into the asymptotic behavior of the exact wave function at both small and large distances, motivating the development of a few parametric Ansatz which is locally accurate and yields to a fast convergent basis set. To validate its efficacy, we assess its convergence rate using a toy model of Nuclear Physics, specifically for Deuteron. Furthermore, we employ the expansion of the energy close to the threshold to derive an analytical formula for the binding energy of the Deuteron whose accuracy improves as the effective parameter approaches the critical. To conclude our study, we test the ability of our Ansatz to describe relativistic corrections into a quantum dot and its performance as an orbital in the exploration of the electronic structure of a two-electron quantum dot.</p>","PeriodicalId":182,"journal":{"name":"International Journal of Quantum Chemistry","volume":"124 15","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/qua.27458","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Quantum Chemistry","FirstCategoryId":"92","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/qua.27458","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0

Abstract

Gaussian potentials serve as a valuable tool for the comprehensive modeling of short-range interactions, spanning applications from Nuclear Physics to the artificial confinement of electrons within quantum dots. This study focuses on examining the lowest states within Gaussian wells, with particular emphasis on the weakly bound regime. The analysis delves into the asymptotic behavior of the exact wave function at both small and large distances, motivating the development of a few parametric Ansatz which is locally accurate and yields to a fast convergent basis set. To validate its efficacy, we assess its convergence rate using a toy model of Nuclear Physics, specifically for Deuteron. Furthermore, we employ the expansion of the energy close to the threshold to derive an analytical formula for the binding energy of the Deuteron whose accuracy improves as the effective parameter approaches the critical. To conclude our study, we test the ability of our Ansatz to describe relativistic corrections into a quantum dot and its performance as an orbital in the exploration of the electronic structure of a two-electron quantum dot.

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
高斯井中的弱结合态:从氘核结合能到量子点的电子结构
高斯势是全面模拟短程相互作用的重要工具,应用范围从核物理到量子点内电子的人工约束。本研究重点考察高斯井内的最低态,尤其关注弱约束机制。分析深入探讨了精确波函数在小距离和大距离时的渐近行为,从而开发出一种局部精确并能产生快速收敛基集的少数参数解析法。为了验证其有效性,我们使用一个核物理玩具模型(特别是氘核模型)来评估其收敛速度。此外,我们还利用接近临界值的能量扩展,推导出氘核结合能的解析公式,其精确度随着有效参数接近临界值而提高。在研究的最后,我们测试了我们的 "反演 "对量子点相对论修正的描述能力,以及它在探索双电子量子点电子结构中作为轨道的性能。
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
International Journal of Quantum Chemistry
International Journal of Quantum Chemistry 化学-数学跨学科应用
CiteScore
4.70
自引率
4.50%
发文量
185
审稿时长
2 months
期刊介绍: Since its first formulation quantum chemistry has provided the conceptual and terminological framework necessary to understand atoms, molecules and the condensed matter. Over the past decades synergistic advances in the methodological developments, software and hardware have transformed quantum chemistry in a truly interdisciplinary science that has expanded beyond its traditional core of molecular sciences to fields as diverse as chemistry and catalysis, biophysics, nanotechnology and material science.
期刊最新文献
Issue Information The Interaction Between Fluorinated Additives and Imidazolyl Ionic Liquid Electrolytes in Lithium Metal Batteries: A First-Principles Study Prediction of Molar Entropy of Gaseous Molecules for a New Pὃschl-Teller Potential Model ISI Energy Change Due to an Edge Deletion First-Principles Study on Electronic and Optical Properties of Novel Potential Photocatalytic Water-Splitting Material: Blue-P/Hf2CO2 vdW Heterostructure
×
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