KFC
Mar31-09, 11:52 PM
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
\overline{(\Delta n_r)^2} = -\frac{1}{\beta}\frac{\partial \bar{n}_r}{\partial \epsilon_r}
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
\overline{(\Delta N)^2} = \overline{(N-\overline{N})^2}
but how do you find the maximum?
\overline{(\Delta n_r)^2} = -\frac{1}{\beta}\frac{\partial \bar{n}_r}{\partial \epsilon_r}
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
\overline{(\Delta N)^2} = \overline{(N-\overline{N})^2}
but how do you find the maximum?