A system at time t = 0 is in the state |ψ> = a|E1> + b|E2>, where |E1> and |E2>
are (normalised) energy eigenstates with two different energies E1 and E2, and a, b
are real numbers. Write down the state |ψ, t> for the system at time t. What are the
probabilities at time t to find the system in the states |E1>, |E2> and (|E1>+|E2>)/√2?
The Attempt at a Solution
I believe I've correctly found that the probability to find the system in ether |E1> or |E2> is |a|^2 or |b|^2 respectively independent of time, as solving the TDSE for |ψ> shows that only the phase of a(t), b(t) changes with time. If this is wrong please tell me so i can post my full working!
My question though, is if i've correctly interpreted "find the system in the states" to mean "measure the energy of the system to be", then isn't the probability of finding the system in a superposition of eigenstates 0, as when we measure the superposition of eigenstates collapses into only a single one, so we must obtain either |E1> or |E2>?
Thanks in advance for your help.