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Second quantisation formula (electron-phonon coupling)

  1. Jun 6, 2015 #1
    Hello,
    I can't understand where this formula ((8.5), Rössler, Solid State Theory, Springer) comes from (see attached file).
    The label l stands for the electrons positions and c and c dagger are the free electron creation and annihilation operator. This expression is used to write the linear term in the perturbative expansion of the electron-phonon coupling in second quantization.

    Thank you in advance.
     

    Attached Files:

  2. jcsd
  3. Jun 6, 2015 #2
    Sorry, there is a mistake in the formula. The right-hand side is
    ## \sum_\vec{k} c^\dagger_{k+q}c_k ##
     
  4. Jun 7, 2015 #3

    DrDu

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    Science Advisor

    In the sum on the left hand side, it would be more precise to include ## c^\dagger_{r_l}c_{r_l}##. Then use the usual representation of the ##c_r## in terms of the ##c_k##.
     
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