GRE 8677 #96

aby
Posts: 9
Joined: Fri Sep 30, 2011 6:41 am

GRE 8677 #96

Postby aby » Sun Oct 09, 2011 8:08 am

Image

the official solution to this problem is (B). I completely understand why the sum includes only even contributions. my problem with this question is that the sum includes the member n=0, but according to the first order perturbation theory:
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notice that the index i runs on all non-negative integers except for i=n. returning to the question at hand we see that the sum in (B) should really run on all n≠0, and not include the term n=0. but because the sum includes this term, it turns out that (B) is incorrect and thus choice (E) is the answer.
what am i missing?

The_Duck
Posts: 41
Joined: Tue Nov 16, 2010 12:04 pm

Re: GRE 8677 #96

Postby The_Duck » Sun Oct 09, 2011 7:05 pm

You're forgetting that psi^1 is the *correction* to psi^0, the unperturbed state. The full wave function to first order is psi^0 + psi^1.

aby
Posts: 9
Joined: Fri Sep 30, 2011 6:41 am

Re: GRE 8677 #96

Postby aby » Mon Oct 10, 2011 4:46 am

thanks, i probably would waste hours until i would notice my mistake...




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