ehrenfest
Feb29-08, 08:47 AM
1. The problem statement, all variables and given/known data
This question refers to Kittel's solid-state physics book.
I am confused about why you get a set of equations for the central equation. They say that psi_k could equally well be labeled by psi_{k+G}, so isn't the central equation going to be exactly the same when you change k to k+G, except maybe with the index shifted? So, what is the point of writing all those equation that are just cyclic permutations of one another?
Also, can someone explain why they say, in the "Approximate Solution Near a Zone Boundary," that they only retain coefficients in the central equation that contain both coefficieints C(.5G) and C(-.5G)? How do they know that there are no other important coefficients? It seems like they not only use only those two equations, but they set all of the other coefficients to 0 in the two equations that they do use, right? How is that justified?
2. Relevant equations
3. The attempt at a solution
This question refers to Kittel's solid-state physics book.
I am confused about why you get a set of equations for the central equation. They say that psi_k could equally well be labeled by psi_{k+G}, so isn't the central equation going to be exactly the same when you change k to k+G, except maybe with the index shifted? So, what is the point of writing all those equation that are just cyclic permutations of one another?
Also, can someone explain why they say, in the "Approximate Solution Near a Zone Boundary," that they only retain coefficients in the central equation that contain both coefficieints C(.5G) and C(-.5G)? How do they know that there are no other important coefficients? It seems like they not only use only those two equations, but they set all of the other coefficients to 0 in the two equations that they do use, right? How is that justified?
2. Relevant equations
3. The attempt at a solution