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Reciprocal lattice and Fourier series

  1. Nov 17, 2007 #1
    First off, this is not a homework problem. I was reading Charles Kittel solid states book on Chapter 2, equation 3:

    electron number density, n(x), expanded in a Fourier series:

    [tex] n(x) = n_0 + \sum_{p} [C_p cos(\frac{2\pi p x}{a}) + S_p sin(\frac{2\pi p x}{a})] [/tex]

    From this expansion, wouldn't the density n(x = 0) be infinity ? since [tex]C_p[/tex] shouldn't be zero for the Fourier expansion to make sense.
    Last edited: Nov 17, 2007
  2. jcsd
  3. Nov 17, 2007 #2
    Why shouldn't C_p be zero for it to make sense? You realize that the value of C_p depends on p, right? So there could be C_p values which are non-zero and others which are zero.
  4. Nov 19, 2007 #3
    Basically fourier series repersentation is applied to functions which are bounded.The next thing is that you have to check for appropriate Dirichlet's conditions.

    Thus at the very beginning, a peassumption for applying fourier series expansion is that the function it represents is always finite.
    More simply speaking, kanato is right.
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