1. The problem statement, all variables and given/known data If the system is in a state |ψ> = 1/sqrt(6) |v1> + 1/sqrt(3) |v2> - i/sqrt(2) |v3> with Hamiltonian satisfying H|vj> = (2-j)a|vj> Find the mean value of energy <E> and the root mean square deviation √(<E2> - <E>2 ) that would result from making a number of measurements of the energy of the system in state |ψ> 2. Relevant equations <E> = <ψ|E|ψ> for a free particle E = p2 / 2m 3. The attempt at a solution To find the mean value of Energy <E> is it just eigenvalues (a, 0 -a) multiplied by the probability of it being in the corresponding state P = (1/6, 1/3, 1/2)? = a/6 - a/2 = -2a/6. For E2 then do you just have the same, but the eigenvalues squared multiplied by the probabilities?