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
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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.

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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。
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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.
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