I was reviewing the infinite square well, using D.J. Griffiths, and came across this small point of confusion. The time-independent solution is shown to be Asin(kx), where the constant A is determined by normalization. Then, in assembling the complete (time dependent) solution, he writes that the most general solution "is a linear combination of stationary states", where each stationary state is assigned a coefficient c_n. Griffiths then explains that |c_n|^2 is the probability of observing that state, and "the sum of all these probabilities should be 1." My confusion is this: if c_n is the probability of observing each state, why do we use the normalization requirement to find A? Isn't this in effect normalizing twice?