A particle is in an infinite square well extending from x = 0 to x = a. Its state is a
linear combination of the two lowest energy states.
Psi(x, t) = A(2 Psi1(x, t) + Psi2(x, t))
a) If a measurement of energy is made what are the possible results of the measurement?
What is the probability associated with each? What is the average value of energy?
The Attempt at a Solution
I know that when the Hamiltonian operates on Psi_n(x,t) it give E_n Psi_n(x,t), right? So are the possible results just Psi1(x,t) and Psi2(x,t) or would they be 2A E1 Psi1(x,t) and A E2 Psi2(x,t)? I am confused because I know quantum state vectors are supposed to be normalized but I am confused how that translates to wave functions?
And as for the probability, I really am not sure where to start can someone point me in the right direction?
Thanks for the help