According to [Wikipedia][1], if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state.

Now consider state $\left|\Psi\right>=(\left|\psi_1\right>+\left|\psi_2\right>)/\sqrt2$, which is a superposition. Let $\left|\psi_i\right>$ be eigenstates of Hamiltonian. Then measurements of energy will give $50\%$ chance of it being $E_1$ and $50\%$ of being $E_2$. But this then corresponds to the definition above of mixed state! At the same time superposition is defined to be a pure state.

So, what is the mistake here? What is real difference from mixed state and superposition of pure states?


  [1]: http://en.wikipedia.org/wiki/Density_matrix#Pure_and_mixed_states