Let O be an operator which commutes with the Hamiltonian H . This implies that we can have common eigenstates of O and H . Assume that our system is in one of these common eigenstates. If we measure of O , it will definitely yield an eigenvalue q (the good quantum number). Also, it is a well-known result that an eigenstate of the Hamiltonian is a stationary state, which means that even if the system is left to evolve for some time before the measurement is made, it will still yield the same eigenvalue. Therefore, If our system is in a common eigenstate, its eigenvalues of O (good quantum numbers) won't change with time.