1. The problem statement, all variables and given/known data Suppose that |i> and |j> are eigenkets of some Hermitian operator. Under what condition can we conclude that |i> + |j> is also an eigenket of A? Justify your answer. 2. Relevant equations It seems that all that is needed is for "A" to be a linear operator and for |i> and |j> to have the same eigenvalue. Justification: A(u + v) = Au + Av (that's A's linearity at work) Au = u*u Av = v*v If we have u = v (matching eigenvalues), then: A(u + v) = u*(u + v) = v*(u + v) ...and thus: A(u + v) = [some common scalar]*(u + v) ...meaning (u + v) is eigenstate of linear operator "A". My question: qed?