The eigenvalues of which are E 1 and E 2 and the eigenvectors, ( 1 0 ) and ( 0 1 ) . These two eigenvectors designate the two states of the system. If the system is prepared in either of the states it would remain in that state. If E 1 happens to be equal to E 2 there will be a twofold degeneracy in the Hamiltonian. In that case any superposition of the degenerate eigenstates is evidently another eigenstate of the Hamiltonian. Hence the system prepared in any state will remain in that forever.