First off sorry for the badly worded title. 1. The problem statement, all variables and given/known data Beginning of Question: Consider a single quantum particle of mass M trapped in the infinite square well potential, V(x), given by V(x)= 0 if 0 < x < L infinity otherwise The wave function for a particle in the n-th energy level is: Ψn(x) = √(2/L) sin(nπx/L) a.) I found the expected position and momentum of a particle in the n-th energy level. b.) I calculated the expectation value for the energy of a particle in the n-th energy level using the hamiltonian. Bit of Question I'm stuck on: c.) Suppose that the particle initially starts in the lowest energy level and the potential is instantaneously changed to: V(x) = 0 if 0 < x < L/2 infinity otherwise Find the probability that the particle ends up in the lowest energy level of the new potential. 2. Relevant equations 3. The attempt at a solution. I'm not exactly sure what to do here. I assume it must be something along the lines of: 1st - Finding the lowest allowed energy level 2nd - Finding the probability that the particle would be in this state. I was thinking that I might be able to use a method along these lines: Renormalise the wave equation first to account for the change in potential? Then repeat what I did in part b.) to find the expectation value of the energy of the particle in the n-th energy level? I would surely then be able to find the lowest expected value for the energy? And then I would be able to find the probability that a particle is in that state? Or have I got totally the wrong idea here? It seems as though I'm ignoring the fact that the potential changed instantaneously.