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>
<E> = <ψ|E|ψ>
for a free particle E = p2 / 2m
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?