Energy Measurements of Particle in Superposition of States

[gysush]

Given that E(n) = (n^2)E, and that our wave function PSI = 1/Sqrt(14)(Psi(1) + 2*Psi(2) + 3*Psi(3), what is the the value for the measurement of the energy?


So, <H> = SUM((c(n)^2)*E(n))

where E(n) = (n^2)*E and c(1)=1/sqrt(14), c(2)=2/sqrt(14), c(3)=3/sqrt(14), which satisfies SUM(c(n)^2) = 1

Thus, <H> =

= 1/14*(E + 4*4*E + 9*9*E) = 7*E

but the answer key says 9*E...what am I doing wrong?

 

[ideasrule]

That should be right, unless we're both missing something obvious (not outside of realm of possibility for me...)

 

[vela]

Looks right to me too.