Abstract: 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.

Key words: quantum mechanics, operator, system of eigenfunctions, commutation