对于自旋量子数为二分之一的自旋角动量态空间中的任何一个纯态，皆可找到自旋角动量在某一个方向上的分量算符，使得此纯态是这个分量算符的本征态.但是对于量子数为 1 或更大的角动量的态空间中的纯态，发现只有一部分态有相应的结论.由此便可把纯态分为两类.进而可对这两种不同的纯态的存在性、制备方法进行探讨.发现对于不能成为角动量某一方向上分量算符的本征态的态，没有很好的试验方法对其进行制备，这便为实验物理学家提出了一个棘手的问题.

For any pure state in the state space of spin angular momentum with spin quantum number

0.5，the component operator of spin angular momentum along a certain direction can be

found，and the pure state is the eigenstate of the component operator. However，for the pure

state in the state space of spin angular momentum with quantum number 1 or more，it is found that

only some states have corresponding conclusions. Therefore，pure states can be divided into two

categories. The existence and preparation methods of these two different pure states are dis-

cussed. It is found that there is no good experimental method to prepare the eigenstates which

cannot be the compo- nent operators of angular momentum in a certain direction，which poses a

thorny problem for experimental physi-cists.