量子体系的幺正变换算符的性质研究  

Study on the Properties of Unitary Transformation

作　　者：冯伟鑫 张海丰[1] 刘明达[2] 韩海生[1] 李慕勤[3] FENG Wei-xin;ZHANG Hai-feng;LIU Ming-da;HAN Hai-sheng;LI Mu-qin(Jiamusi University School of Science,Jiamusi Heilongjiang 154007,China;Jiamusi UniversityThe Second Affiliated Hospital,Jiamusi Heilongjiang 154007,China;Jiamusi UniversityAcademy of Materials Science,Jiamusi Heilongjiang 154007,China)

机构地区：[1]佳木斯大学理学院,黑龙江佳木斯154007 [2]佳木斯大学附属第二医院,黑龙江佳木斯154007 [3]佳木斯大学材料科学院,黑龙江佳木斯154007

出　　处：《佳木斯大学学报（自然科学版）》2020年第5期165-167,共3页Journal of Jiamusi University：Natural Science Edition

基　　金：黑龙江省省属本科高校基本科研业务费科研项目资助(2019-KYYWF-1363);佳木斯大学大学生创新创业训练计划项目(2019xj25)。

摘　　要：利用表象理论给出了不同表象之间的幺正变换关系,讨论了幺正变换下算符本征值、矩阵的迹、力学量的取值几率和力学量的期望值等性质,最后给出了幺正变换算符和厄米特算符及能量算符之间的关系。研究结果标明幺正变换后本征值、矩阵的迹、取值几率和期望值都不改变;幺正变换算符和厄米特算符及能量算符的关系分析对加深幺正变换的理解有重要作用。Based on the representation theory,the unitary transformation relations between different representations are given,the eigenvalue of the operator under unitary transformation,the trace of the matrix,the probability of the value of mechanical quantities and the expected value of mechanical quantities are discussed,and the relations between unitary transformation operators,Hermitian operators and energy operators are given.The result shows that the eigenvalue,trace of matrix,value probability and expected value do not change after unitary transformation.The analysis of the relation between unitary transformation operator and Hermitian operator and energy operator is very important to deepen the understanding of unitary transformation.

关 键 词：表象理论 幺正变换算符 厄米特算符 能量算符 

分 类 号：O431[机械工程—光学工程]