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Statistical deviation

  1. Mar 31, 2009 #1


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    For some given statistics (e.g. Fermi-Dirac or Bose-Einstein), once we know the average number of particles at state r, it is easy to calculate the dispersion by calculating

    [tex]\overline{(\Delta n_r)^2} = -\frac{1}{\beta}\frac{\partial \bar{n}_r}{\partial \epsilon_r}[/tex]

    and the total number of particle is just the sum of all average number of particles.

    My question is: how do you find maximum dispersion of TOTAL NUMBER (N)?

    I know
    [tex]\overline{(\Delta N)^2} = \overline{(N-\overline{N})^2}[/tex]

    but how do you find the maximum?
  2. jcsd
  3. Apr 1, 2009 #2


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    For fermi stat., the total number of particles is
    [tex]N = \sum_r \overline{n}_r[/tex]

    so how to calculate [tex]\overline{N}[/tex] ?
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