# Condensed matter-integral over density of states

condensed matter--integral over density of states

## Homework Statement

http://online.physics.uiuc.edu/courses/phys460/fall06/handouts/460-lect12.pdf [Broken]

Could someone explain to me why the first equation on slide 22 is true?

## The Attempt at a Solution

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malawi_glenn
Homework Helper
you mean:

Quantitative evaluation?

you mean:

Quantitative evaluation?
What? I mean I don't understand why it is true. It is also on page 142 of Kittel.

malawi_glenn
Homework Helper
What? I mean I don't understand why it is true. It is also on page 142 of Kittel.
Oki I just mean the eq under that headline.

any way here it goes:

take eq 24 on p 142. and read the 3lines above it.

What is the fermi dirac distribution at T = 0K? well f (T goes to 0) = 1.. (see eq 5 p.136 and take limit t goes to 0).

and you only have to integrate up to the fermi energy at 0K due to the density of state function. see fig 5 p.140.

Oki I just mean the eq under that headline.
What is the fermi dirac distribution at T = 0K? well f (T goes to 0) = 1.. (see eq 5 p.136 and take limit t goes to 0).
f (T goes to 0) = 1 only if mu > epsilon

malawi_glenn
Homework Helper
Oh yes, it meant when kT << E_f

:)

Oh yes, it meant when kT << E_f

:)
Why does that imply that mu is greater than epsilon?

Oki I just mean the eq under that headline.
Oh--yes it is the equation under that headline--sorry.

see fig 5 p.140.
I see,the area of region 1 must be the same as the area of region 2.