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Homework Help: Kinetic energy of a free electron in a lattice

  1. Feb 10, 2014 #1
    1. The problem statement, all variables and given/known data
    Show that for a simple square lattice (in 2-D) with the lattice spacing = a, the kinetic energy of a free electron at a corner (point A in the figure below) of the first Brillouin zone is higher than that of an electron at the midpoint of a side of the zone (point B in the figure below) by a factor of 2.
    http://imageshack.com/a/img856/2000/zuci.jpg [Broken]

    2. Relevant equations

    No clue

    3. The attempt at a solution

    So...like I have no clue about this...has anyone got a hint for me? I dont even know which equations to use...thanks guys...
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Feb 11, 2014 #2


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    Gold Member

    I guess this is quantum mechanics applied to solid physics?
    In QM, electrons can't be totally at rest, which gives some sense to the question ...
    You need first to remember everything about what a Brillouin zone is!
    Then you simply need to translate "corner" and "midpoint" to answer this question.

    This question contains little very physical meaning.
    It is more a check that you know what a Brillouin zone is.
    Therefore, I also suggest you the question yourself about why this concept (Brillouin zone) emerged and what its utility is.
    This might help you for the next questions, maybe?
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