动力学矩阵方程法求解一维至三维晶格声子色散关系  

Solution of dynamic matrix equation of phonon dispersion relations in one-dimensional tOthree-dimensional lattice

作　　者：鲁勇 LU Yong(College of Mathematics and Physics,Beijing University of Chemical Technology,Beijing 100029,China)

机构地区：[1]北京化工大学数理学院,北京100029

出　　处：《大学物理》2024年第9期15-19,45,共6页College Physics

基　　金：国家自然科学基金(12074028)资助。

摘　　要：本文通过动力学矩阵方程求解了一维到三维晶格振动的声子色散关系.与传统的本科生固体物理课程中通过哈密顿正则方程方法求解一维原子链经典模型相比,构建动力学矩阵,使得从一维拓展到三维晶格声子色散关系的求解方程在形式上更具有统一性和普适性,有助于从思维方式上建立一维到三维晶格振动的连续的物理图像.在数值求解三维晶格振动以及考虑非谐效应的影响时,该方法亦提供了更好的便利性.In this paper,the phonon dispersion relation of lattice vibrations from one-dimension tOthree-dimension is solved by constructing dynamic matrix equation.Compared tOtraditional method of solving one-dimensional atomic chain classical model using Hamilton’s canonical equations in solid state physics courses,constructing a dynamic matrix provides a more unified and universal form for solving phonon dispersion relation from one-dimensional tOthree-dimensional lattice.It is helpful tOestablish a continuous physical picture of one-dimensional tOthree-dimensional lattice vibration from the way of thinking.In terms of numerically solving three-dimensional lattice vibrations and considering the effects of anharmonicity,this method alsOoffers greater convenience.

关 键 词：晶格振动 动力学矩阵方程 声子色散关系 

分 类 号：O482[理学—固体物理]