关于表象变换的一点注解  

A Remark on the Transformations Between Different Representations

作　　者：张跃[1] ZHANG Yu(College of Physics and Information Science,Hunan Normal University,410081,Changsha,Hunan,PRC)

机构地区：[1]湖南师范大学物理与信息科学学院,湖南省长沙市410081

出　　处：《曲阜师范大学学报（自然科学版）》2019年第1期74-76,共3页Journal of Qufu Normal University(Natural Science)

摘　　要：分别研究了自旋算符及其本征函数从Sz表象到Sx表象的变换.研究表明,利用由^Sx的本征函数的表象变换式计算得到的变换矩阵和喀兴林(1988)中的变换方法进行自旋分量算符的变换,变换结果中出现一个与^Sx和^Sz的对易关系不相融洽的负号;此外,该变换矩阵不能应用于^Sz或者^Sy的本征函数从Sz表象到Sx表象的变换.阐明了一个算符及其本征函数的表象变换矩阵应该由该算符自己的本征函数从旧表象到新表象的变换定义式确定.The paper studies the transformations of spin operators as well as their eigenfunctions from Szto Sxrepresentation.The research demonstrates that if using the matrix of obtaining from the equation of transforming the eigenfunctions of^Sxand in terms of the transformation arising from Ke Xinglin(1988)for all of the spin operators fromSzto Sxrepresentation,a negative symbol will occur in the result,which is not concordant with the commutation relation between^Sxand^Sz.Moreover,this matrix can not be applied to the transformation of the eigenfunctions of^Szor^Sy.We conclude that with respect to the transformation of representation of an operator and its eigenfunctions,the matrix of transformation should be obtained from the equation of transforming the eigenfunctions of the same operator from the old to the new representation.

关 键 词：表象变换 数学定义 变换矩阵 旧表象 新表象 

分 类 号：O413.1[理学—理论物理]