Hermite矩阵酉相似对角化的物理意义

量子力学中的一项基本假定是代表力学量的算符是Hermite算符,由力学量算符的本征方程解出的全部本征值,就是相应力学量的可能取值。如果用测量仪器测量这个力学量的取值,只能测得其本征值。本文先从数学上严格证明了Hermite矩阵可以酉相似对角化,然后结合物理实例分析了其物理意义。

Thephysical meaning of a Hermite matrix being similar to the diagonal matrix

The mechanical quantity is expressed by a Hermite operator is one of the basic hypotheses of quantum mechanics.All eigenvalues solved by the mechanical quantity operator eigenvalue equation are the possible values of the corresponding mechanical quantities.If one with a measuring instrument to measure the amount of value,eigenvalues can only be measured.In this paper,a Hermite matrix being similar to a diagonal matrix is proved in mathematics,and then combined with examples to explain its physical meaning.