Condensed matter-integral over density of states

In summary, the content discussed in the conversation is related to condensed matter and the integral over density of states. The first equation on slide 22 is true because of the fermi dirac distribution at T = 0K, where f (T goes to 0) = 1. This is also shown on page 142 of Kittel's book. The equation under the headline must also be considered and the density of states function must be integrated up to the fermi energy at 0K. This implies that mu is greater than epsilon. The area of region 1 must be the same as the area of region 2.
  • #1
ehrenfest
2,020
1
condensed matter--integral over density of states

Homework Statement


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

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


Homework Equations





The Attempt at a Solution

 
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  • #2
you mean:

Quantitative evaluation?
 
  • #3
malawi_glenn said:
you mean:

Quantitative evaluation?

What? I mean I don't understand why it is true. It is also on page 142 of Kittel.
 
  • #4
ehrenfest said:
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.
 
  • #5
malawi_glenn said:
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
 
  • #6
Oh yes, it meant when kT << E_f

:)
 
  • #7
malawi_glenn said:
Oh yes, it meant when kT << E_f

:)

Why does that imply that mu is greater than epsilon?
 
  • #8
malawi_glenn said:
Oki I just mean the eq under that headline.

Oh--yes it is the equation under that headline--sorry.
 
  • #9
malawi_glenn said:
see fig 5 p.140.

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

What is condensed matter-integral over density of states?

Condensed matter-integral over density of states is a concept in condensed matter physics that describes the total number of allowed energy states in a material or system. It is often represented as a function of energy and is used to study the electronic and magnetic properties of materials.

What is the importance of studying condensed matter-integral over density of states?

Studying condensed matter-integral over density of states is important because it allows scientists to understand the fundamental properties and behaviors of materials at the atomic and subatomic level. This information is crucial for developing new materials with specific properties and for improving existing technologies.

How is condensed matter-integral over density of states calculated?

Condensed matter-integral over density of states is typically calculated using mathematical models and equations that take into account the energy levels and interactions between particles in a material. These calculations can also be done experimentally by measuring the energy levels of a material using techniques such as spectroscopy.

What factors can affect the condensed matter-integral over density of states?

The condensed matter-integral over density of states can be affected by various factors, such as temperature, pressure, and the composition of the material. Changes in these parameters can alter the energy levels and interactions between particles, resulting in a different density of states.

How does condensed matter-integral over density of states relate to other properties of materials?

Condensed matter-integral over density of states is closely related to other properties of materials, such as conductivity, magnetism, and thermal behavior. By understanding the density of states, scientists can gain insights into how these properties emerge and how they can be manipulated for practical applications.

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