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Suppose a particle of mass m is sitting in the ground state of a 1-dimensional box of length L. The length of the box is suddenly doubled, and the energy of the particle is measured. What is the probability that the particle will be found in the second excited state of the box?

I know the particle initially has some energy corresponding to the first energy level in the initial box, and I can calculate the energy corresponding to the third energy level (second excited state) in the new box. To solve the problem I need to the new wavefunction for the particle. So I'm going to have something (I think) like [tex]A \sin frac{n \pi x}{L}[/tex]. The only problem is I don't know how to get A... I can't just normalize it, because I'd get a probability of one. Any pointers?