# Condensed matter-integral over density of states

1. Mar 24, 2008

### ehrenfest

condensed matter--integral over density of states

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 3, 2017
2. Mar 24, 2008

### malawi_glenn

you mean:

Quantitative evaluation?

3. Mar 24, 2008

### ehrenfest

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

4. Mar 24, 2008

### malawi_glenn

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.

5. Mar 24, 2008

### ehrenfest

f (T goes to 0) = 1 only if mu > epsilon

6. Mar 24, 2008

### malawi_glenn

Oh yes, it meant when kT << E_f

:)

7. Mar 24, 2008

### ehrenfest

Why does that imply that mu is greater than epsilon?

8. Mar 24, 2008

### ehrenfest

Oh--yes it is the equation under that headline--sorry.

9. Mar 24, 2008

### ehrenfest

I see,the area of region 1 must be the same as the area of region 2.