Consider a quantum particle confined in the infinite square potential well shown in the figure. If x ≤ 0 and x ≥ L, V(x) = ∞. If 0 < x < L, V(x) = V0. Write down the general expressions for the energy eigenvalues En and the energy eigenstates ϕn(x). Calculate the time evolution for the initial quantum state ψ(x, 0) = 1/5(3 ϕ1(x) + 4ϕ2(x)). Calculate the momentum expectation value ⟨p⟩ at t = 0. If an experimentalist attempts to measure the momentum of the particle at t = 0, what are the possible measurement outcomes and the probability for each?
