Statistical Mechanics/Density of States  From Wikibooks, open
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navigation, search  Thermal Average Number of Particles
Distribution Function[edit]  f(\epsilon) \equiv \ \langle
N(\epsilon) \rangle  Now, since this is a distribution function,
we can find thermal average quantities of other thermodynamic
quantities:  \langle X \rangle = \sum _n f(\epsilon _n,T,\mu)X
_{n}  Where n denotes the quantum orbital.  Now if the orbital
step, n, is small, we can change the sum to an integral:
\langle X \rangle =  \int d\epsilon
D(\epsilon)f(\epsilon,T,\mu)X(\epsilon)  Here, this  D(\epsilon)
function is the function that mathematically allows us to
transform the sum to the simplest possible integration (In the
Thermal Radiation case, we will see that the D function is the
Jacobian to spherical coordinate).  It is also better known as
the...  Density of States[edit]  The mathematics of the DoS were
explained in the previous section, all that remains of
importance i