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## Homework Statement

If the system is in a state

|ψ> = 1/sqrt(6) |v1> + 1/sqrt(3) |v2> - i/sqrt(2) |v3>

with Hamiltonian satisfying H|v

_{j}> = (2-j)a|v

_{j}>

Find the mean value of energy <E> and the root mean square deviation √(<E

^{2}> - <E>

^{2}) that would result from making a number of measurements of the energy of the system in state |ψ>

## Homework Equations

<E> = <ψ|E|ψ>

for a free particle E = p

^{2}/ 2m

## The Attempt at a Solution

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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 E

^{2}then do you just have the same, but the eigenvalues squared multiplied by the probabilities?