Hope that HW #3 is going well.
I had one correction for prob. 1. Please check the correction at the Homework part of the course web site. Download the new pdf file that includes the correction. Thanks, K, for your pointing this problem out in class.
Any questions about this homework?
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I have a quesion regarding problem 3 (part b) in homework 4. My solution for w_k , with k=Pi/a is complex... can anyone offer advice while I try to figure out what is going on?
ReplyDeleteAlso, I have that the two branches for w_k are the same magnitude, but opposite sign and feel uncertain about how different this is from what we worked on in class.
w_k for any k must be real. So, it seems that you need to check your solution for part A. It is likely that your matrix was set up incorrectly. The equation of motion must be in the form of A b = 0 where A is a Hermitian 2x2 matrix, and b is a two dimensional real vector (u and v are its components). I hope this makes sense.
ReplyDeleteReferring to equations 12 and 13 on page 650 (in Appendix C), what is the significance of the kronecker-delta selecting -k = k' ? Why not +k?
ReplyDeleteIf you read Lecture 06.pdf, page 2, you will find "Some Important Math." The first identity in the table is the one that is relevant here. Specifically the G = 0 case is used here (as it can be). For instance, in equation (12) that you are discussing, -(k+k') corresponds to my k in my lecture note. So, k+k'=0, which means -k=k'. So, it is definitely not k=k'! Hope this helps.
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