两个力学量算符具有共同本征态系的条件

Study on existence of a simultaneous system of eigenfunctions of two operators

量子力学是人们了解微观世界的一门重要的课程.在量子力学中,由于任何实物体都具有波粒二象性,必须用算符来表示力学量,因此算符理论显得尤为重要.在研究多个算符时,有一个非常重要的定理:两个力学量算符能够具有共同本征函数系的充分必要条件是这两个个力学量算符能够互相对易.本文分析了在使用该定理时可能存在的一些问题,并对这些问题进行了澄清.

The quantum mechanics is an important course that one can understand the microcosmic world. Because of wave-particle duality for system with finite rest mass in quantum mechanics and then replaced each of mechanical quantities by its corresponding operator, the operator theory seems to be important particularly. There is an important theorem when we study many operators, namely, the necessary and sufficient condition for the existence of a simultaneous system of eigenfunctions of two operators is that they can commutate each other. These problems are analyzed and cleared when we used the theorem to solve it.