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Free electron square lattice

  1. Oct 5, 2013 #1
    1. The problem statement, all variables and given/known data
    Show for a simple square lattice that the kinetic energy of a free electron is higher at the corner of the first zone than at the midpoint a side face by a factor of 2.


    2. Relevant equations
    Simple geometry.


    3. The attempt at a solution
    I think I know how to solve, but I am not completely sure I understand the question. The position of the electron refers to the position of its k-vector in k-space right? Well this is not real space, and I cant really see how this has anything to do with the lattice being square in real space.
     
  2. jcsd
  3. Oct 6, 2013 #2

    Physics Monkey

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    I suspect the hidden assumption here is that you should use a tight binding model with nearest neighbor hopping on the lattice given. So in your case the square lattice is specifying the shape of the Brillouin zone and telling you the energy spectrum.

    Does this help?
     
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