Problem 6 ended a little abruptly and without comment. The result indicates that to linear order in alpha, the energy of the ground state is changed from its pure infinite-square-well value by the amount 2*alpha/L. Note that this is the expectation value of the small delta function potential in the ground state of the infinite square well (since sin (pi x/L) =1 in the center and the normaling factor is Sqrt(2/L), which gets squared in the expectation value calculation. This is a pretty simple result, and this apparent coincidence is probably something we should explore and use more if we get a chance.
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ReplyDeleteIs there supposed to be a page with 4d and 5 on them?
ReplyDeleteNo, there is no page missing.
ReplyDelete4d is an open-ended discussion question, hence no solution and well, 5,...I think you might have an idea what happens in 5. What do you think? What are some possible choices for approaching that?