Hwang Tsung-Min, Wang Wei-Hua, Wang Weichung
Department of Mathematics, National Taiwan Normal University, Taipei 116, Taiwan.
J Nanosci Nanotechnol. 2008 Jul;8(7):3695-709.
Electronic states in coupled quantum dots are studied numerically and qualitatively in this article. A second-order finite volume scheme based on uniform meshes is first developed to solve the three-dimensional Schrödinger equation. The scheme is used to solve the eigenvalue problem with more than 12 million unknowns. Using these efficient numerical tools, we study quantum structure induced interactions, with emphases on the effects of dot size and space layer thickness. The numerical experiments have predicted the phenomena that envelope functions become delocalized over two QDs and the energy levels show anticrossing behavior.
本文对耦合量子点中的电子态进行了数值和定性研究。首先开发了一种基于均匀网格的二阶有限体积格式来求解三维薛定谔方程。该格式用于求解具有超过1200万个未知数的特征值问题。利用这些高效的数值工具，我们研究了量子结构诱导的相互作用，重点关注量子点尺寸和空间层厚度的影响。数值实验预测了包络函数在两个量子点上离域化以及能级出现反交叉行为的现象。
