Let say I have prepared two identical particle, both describable by a wavefunction Psi, whereby, Psi = a*1 + b*2, where, 1 and 2 are two stationary wavefunctions. If I perform an experiment to find out the systems' energy, this is equivalent to operating a Hamiltonian on Psi. Operating, HPsi = H(a*1 + b*2) = a*E1*1 + b*E2*2 where, E1 is eigenvalue with eigenfunction 1, E2 = eigenvalue with eigenfunction 2. That means, I might get energy = E1 for the first particle from the experiment, and energy = E2 for the second particle. How can we get two different energy value E1 and E2 when I prepared both the particles exactly the same and both have the same wavefunction. So they must give me the same energy. Otherwise, where does the energy difference E1-E2 come from?"