计算机分析球形量子点模型的符号-数值算法
Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models
摘要：
本文提出了一种用不同的单参数基函数求解轴对称封闭势椭圆边值问题的计算方法。所提出的符号-数值算法在Maple中实现的效率是通过球形量子点模型的例子来显示的，对于该模型，在传统的有效质量近似下计算了能量谱和本征函数与球形纵横比的关系。利用精确分类和绝热分类揭示了强维量子化体系中有限壁势模型的离散谱转变为连续谱的临界纵横比。
英文摘要：
A computation scheme for solving elliptic boundary value problems with axially symmetric confining potentials using different sets of one-parameter basis functions is presented. The efficiency of the proposed symbolic-numerical algorithms implemented in Maple is shown by examples of spheroidal quantum dot models, for which energy spectra and eigenfunctions versus the spheroid aspect ratio were calculated within the conventional effective mass approximation. Critical values of the aspect ratio, at which the discrete spectrum of models with finite-wall potentials is transformed into a continuous one in strong dimensional quantization regime, were revealed using the exact and adiabatic classifications.
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