1. The problem statement, all variables and given/known data A particle at time zero has a wave function Psi(x,t=0) = A*[phi_1(x)-i*sin(x)], where phi_1 and phi_2 are orthonormal stationary states for a Schrodinger equation with some potential V(x) and energy eigenvalues E1, E2, respectively. a) Compute the normalization constant A. b) Work out Psi(x,t) c) Compute <H> for Psi(x,t) d) Compute delta_E, the energy uncertainty 2. Relevant equations Delta_E = Sqrt(<E^2>-<E>^2) 3. The attempt at a solution a) Set: 1 = <Psi(0)|Psi(0)> => A = 1/sqrt(2) b) From previous: Psi(x,t=0) = 1/sqrt(2)*[phi_1 - i*phi_2] Use the time evolution equation: Psi(x,t) = 1/sqrt(2)*[phi_1*e^(-i*E1*t/h-bar) - i*phi_2*e^(-i*E2*t/h-bar)] c) Probability of measuring E1: P1 = |<phi_1|Psi(x,t)>|^2 = 1/2 Similarly, Probability of measuring E2: P2 = 1/2 Then <H> = P1*E1 + P2*E2 = (E1+E2)/2 d) For this one, I attempted to use the mentioned equation. However, I could not find <E^2>. I thought it would be: (P1*E1)^2 + (P2*E2)^2, but this yields a negative values under the square root, which is not possible since the energy uncertainty is probability not imaginary. Please help, thank you.