Density of states free electron gas

  1. For a free electron gas the procedure for determining the density of states is as follows.
    Apply periodic boundary conditions to the free electron waves over a cube of side L. This gives us that there is one state per volume 2[itex]\pi[/itex]/L3=2[itex]\pi[/itex]/V
    And from there we can find the number of states at a given energy E by multiplying by the volume of a sphere at E in k space.
    One big problem with this is however: Why do we assume that material is necessarily a cube? What if we worked with a ball of metal?
     
  2. jcsd
  3. DrDu

    DrDu 4,421
    Science Advisor

    There is a theorem, I think by Sommerfeld, that the boundary becomes unimportant in determining e.g. the DOS in the limit V->infinity
     
  4. DrDu

    DrDu 4,421
    Science Advisor

    I think Ashcroft Mermin may mention the theorem.
     
  5. I am pretty sure they do. But who is the first to come with it?
    I'll check the book.
     
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