The operator theory is a very important part in the quantum mechanics, in which two mechanical quantity operator commutative problem and their simultanious eigenfunctions are difficult points in the operator theory as they are more complex especially in degenerate situation. Moreover, detailed analysis and discussion is not given in many traditional textbooks. In this paper, a simple proof that two commutative operators can hold the simultanious eigenfunctions in degenerate situation is pres- ented, and we propose two simple methods to solve si...
