Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof of Blochs function.

  1. Oct 4, 2013 #1
    Hi Everybody,

    I am learning solid state physics and read today through Kittel. I am still stuck at the proof of Blochs theorem i.e. the proof of Blochs function.

    For the Schrodinger equation of a periodic potential the general ansatz:

    [tex] \psi = \sum_k C_k e^{ikr} [/tex]

    is made.

    Then, by looking at the Schrodinger equation in the reciprocal lattice, we see that the [itex] C_k [/itex] are a linear combination of [itex] C_{k-G} [/itex], where [itex]G[/itex] is the reciprocal lattice vector.

    Finally, the wave function is indexed by an index [itex] k [/itex] and rewritten as:

    [tex] \psi_k = \sum_G C_{k-G} e^{i(k-G)r}, [/tex]

    where the sum goes now over G.

    I have two questions:
    1) How can we go from the sum over k to a sum over G?
    2) Is [itex] \psi_k [/itex] the same function as [itex] \psi [/itex]? If so, why do we index it with k?

    I hope this is clear enough, and I would be glad for ANY answer!! :)
    I am searching for an ansatz for nearly a week now!!
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: Proof of Blochs function.
  1. Bloch functions (Replies: 5)

Loading...