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Brewer

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Next thing. Can someone point me in the right direction for solving these questions?

Question:

The even parity energy eigenstates for the infinite square well potential, defined by V(x) = 0 for -L/2<x<L/2 and V(x) = infinite otherwise are [tex]\psi_{n}(x) = \sqrt{\frac{2}{L}}cos(\frac{n\pi x}{L})[/tex] with n odd.

a) If the momentum is measure, what values are obtained and with what probability? (Hint: Expand [tex]\psi_{n} (x)[/tex] as a sum of momentum eigenstates)

b) Using the results from a) deduce average p.

c) using symmetry, deduce average x.

Now I know for a) that [tex]\hat{p}u(x) = pu(x)[/tex], but what's u(x)? Where did this come from? What is it? Does it relate to [tex]\psi(x)[/tex] at all? But apart from that I can't work out any other relationships between anything! Any help on these questions would be greatly appreciated. Especially if it can be put really simplisticaly, as I'm struggling somewhat with this course, and neither or my notes or textbook seem to make much sense.