量子体系的幺正变换算符的性质研究

Study on the Properties of Unitary Transformation

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.