In Griffiths' page 36/37 he says "As we'll see in Chapter 3, what |Cn|^2 tells you is the probability that a measurement of the energy would yield the value En (a competent measurement will always return one of the "allowed" values - hence the name - and |Cn|^2 is the probability of getting the particular value En." This statement comes at the end of the infinite square well section and it concerns any sum of stationary states. Wouldn't measuring one of the allowed energies "En", mean collapsing the wave function into the nth stationary state (and that state only!)? Doesn't that mean that the wave function has then assumed a single stationary state, thereby guaranteeing all subsequent energy measurements of the wave function to yield that particular En? This seems to disagree with my intuition about what happens to a wave function after measurement (that it would "delocalize" in energy space) and it disagrees with my professor's interpretation who literally takes issue with the statement that an energy measurement must yield one of the allowed values. He says that it can yield any value, and that a mix/sum of specific n states are responsible for returning a non-"allowed" En.