从量子力学中的表象变换到严格对角化方法  

From the Transformation of Representation in Quantum Mechanics to the Exact Diagonalization Method

作　　者：高雨 关明书 郁华玲[1] GAO Yu;GUAN Ming-shu;YU Hua-ling(School of Physics and Electronic Electrical Engineering,Huaiyin Normal University,Huaian Jiangsu 223300,China)

机构地区：[1]淮阴师范学院物理与电子电气工程学院

出　　处：《淮阴师范学院学报（自然科学版）》2019年第2期110-114,共5页Journal of Huaiyin Teachers College;Natural Science Edition

基　　金：江苏省自然科学基金资助项目(BK20141251)

摘　　要：量子力学中的态矢量和算符一般是放在希尔伯特空间中描述,这种具体的表达方式又被称为表象.从经典的直角坐标系和球坐标系之间的变换出发,讨论了量子力学中的表象变换问题,进而阐述了严格对角化方法的原理.利用严格对角化方法对二维双带正方晶格系统的能谱进行了研究,计算结果表明次近邻格点之间的跳跃势大小对两子带间的能隙起到了调节作用,该结果可以为制备不同的能隙材料提供理论参考.The state vectors and operators were expressed in the Hilbert space, which was called the representation in the quantum mechanics. We discuss the transformation of representation on the basis of the transformation between rectangular axis and spherical coordinate system in the classical mechanics. The principle of exact diagonalization method is discussed, and by which the energy spectrum in a two-band square lattice was investigated. It is found that the gap between two sub-bands is modulated by modulating the next-nearest-neighbor hopping potential, which will give a significant theoretical reference to the observation of experiment.

关 键 词：量子力学 表象变换 严格对角化方法 能隙 

分 类 号：O413.1[理学—理论物理]