量子力学教学中关于自旋算符及其对易关系引入方式的探讨

The Discussion on the Introduction of Spin and Its Commutation Relations in the Teaching Courses of Quantum Mechanics

本文主要探讨了量子力学教学中自旋的一种新的引入方式。通过空间转动变换后粒子内秉空间波函数的转动不变性可以引入自旋算符,由作为矢量的自旋算符平均值的空间转动不变性可以进一步导出自旋算符间的对易关系。这样引入自旋有助于学生认识到空间转动对称性与自旋的关系。

A new way of introduction of spin in quantum mechanics teaching is discussed in this paper. The spin operator is introduced through the spacial rotational invariance of the intrinsic wave function of a particle. Furthermore the commutation relations of the spin operators are introduced through spacial rotational invariance of the average value of the spin operator as a vector. Through this way of spin introduction in teaching it helps the students realize the relation between spacial rotational symmetry and spin.