In case you cannot read it:
Biggerpicture.
Let us suppose that a particle is prepared in the ground state of an infinite square well, which extends from x = 0 to x = L. At t= 0, the potential barrier is removed, causing the particle to suddenly become free. You may assume that the barrier is removed suddenly, so that no work is done in the process. That is, the particle remains in the same energy state before and after the barrier is removed. Think carefully about the problem. At the instant the particle before the Incomes free, what is the wavefunction of the particle? What is the wavefunction the instant after it becomes free? What is the probability that the particle will be found outside the region from x = 0 to x = L at t = 0? Using (a), find phi(k), where Hint: Express sin(z) in terms of complex exponentials eix and e-ix using Euler's identity. Using the result for phi(k) you found in part (b), find the wavefunction psi(x,t) for all subsequent times.