1. The problem statement, all variables and given/known data Hi guys, I've recently taken up quantum, so it's all very new to me, it would be greatly appreciated if someone could check my working! Let ψ1(x) and ψ2(x) be two orthonormal solutions of the TISE with corresponding energy eigenvalues E1 and E2. At time t = 0, the particle is prepared in the symmetric superposition state: and subsequently allowed to evolve in time. What is the average energy of the system as a function of time? What is the minimum time ¿ for which the system must evolve in order to return to its original state (up to an overall phase factor), when it starts in the state ψ(+) (x) Determine the probability to ¯nd the system in the antisymmetric superposition state as a function of time when it starts in the state ψ(+) (x) At time t1 the particle is found in the antisymmetric superposition state. What is the probability to ¯nd the particle in the symmetric superposition state at time t1 + T, where T is the time found above? 2. Relevant equations 3. The attempt at a solution Not sure if the last part is right, as it suggests that the probability of finding the particle in the left half of the box is independent of time! Then again, in an infinite square well the potential doesn't depend on time, so TDSE is reduced to TISE?