Perturbation matrix: free electron model on a square lattice

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Homework Statement


Nearly free electron model in a 2D lattice. Consider a divalent 2D metal with a square lattice and one atom per primitive lattice cell. The periodic potential has two fourier components V10 and V11, corresponding to G = (1,0) and (1,1). Both are negative and mod(V10) > mod(V11).

Write down the secular equation and obtain an expression for the electron energies at k = (pi /a, 0).

Homework Equations




The Attempt at a Solution


Please see attached file (question also attached (part (i). I believe this is wrong but I cannot see what the expectation of the potential between the two final states can be other than zero (as they are separated by a reciprocal lattice vector (0,1).
 

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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
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Fek
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All sorted thank you.
 

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