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Kittel, Chapter 7, Central Equation

  1. Oct 15, 2008 #1
    1. The problem statement, all variables and given/known data
    Kittel states at page 172, that the central equation for the fourier components of waves in a periodic lattice is given by:

    From this he goes on to say "Once we determine the C's from (27), the wavefunctions (25) is given as:


    I'm completely in the blank about how he got the C's isolated and got the above equation for the wavefunction..any help?

    2. Relevant equations

    Equation 27:

    Equation 25:
  2. jcsd
  3. Oct 15, 2008 #2
    He did not actually get the coefficients.
    He even tells you that solving the equation is a very difficult task in general.
    He tells what can be done after the equation is solved.

    About how he gets the wave-function: he assumes that it can be written in the form (25), as a combination of plane waves, with various coefficient. (This form is like a Fourier expansion)
    To find the coefficients, you plug in the function in Schrodinger eq (the one with Bloch functions) and you get some equations for the coefficients.

    This is actually a quite general method of solving differential equations, by using Fourier series. Is not something specific for solid state or Bloch functions.
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