FermiDeriving Fermi Energy from the Total Energy of a Fermi Sphere

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In summary, the conversation is about using the equation E_m=1/n (E)p(E)dE to derive the equation E_m=3/5(E_f). The individual has tried using integration by parts and rearranging the equation, but has been unsuccessful. They are asking for help in showing that the integral in the equation becomes 3/5(Energy) when considering the total energy of a Fermi sphere.
  • #1
cragar
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Homework Statement


use E_m=1/n (E)p(E)dE integral from 0 to Infinity
to derive E_m=3/5(E_f)


Homework Equations


n= p(E)dE integral from 0 to infinty
also n=Q*sqrt(E)dE integarl from 0 to (E_f)
p(E)=Q*sqrt(E)/(e^(E-E_f)+1)


The Attempt at a Solution


i tried doing integration by parts on it and moving stuff around but i can't seem to get it , is there a trick in using that the integral from o to infinty of p(E)dE = 0
 
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  • #2
Please learn to use the latex command here. Otherwise most people won't understand what you are saying and won't help you. I can't even understand half of what you typed out.
 
  • #3
http://en.wikipedia.org/wiki/Fermi_energy
scroll about half way down the page and you will see
total energy of a Fermi sphere , how do i show that , that integral turns into
3/5(Energy)
 

What is the Fermi-sphere derivation and why is it important?

The Fermi-sphere derivation is a mathematical model used to describe the behavior of electrons in a solid material. It is important because it helps us understand the electronic properties of materials, such as their electrical conductivity.

How is the Fermi-sphere derived?

The Fermi-sphere is derived using the principles of quantum mechanics, specifically the Pauli exclusion principle and the Schrödinger equation. These principles allow us to determine the distribution of electrons in energy levels within a solid material.

What factors influence the shape and size of the Fermi-sphere?

The shape and size of the Fermi-sphere are influenced by the number of electrons in the material, the energy of the electrons, and the temperature of the material. It is also affected by external factors, such as the presence of impurities or external electric fields.

What is the Fermi level and how is it related to the Fermi-sphere?

The Fermi level is the highest occupied energy level in a material at absolute zero temperature. It is closely related to the Fermi-sphere, as the Fermi-sphere is a representation of the distribution of electrons around the Fermi level.

How does the Fermi-sphere relate to the concept of band structure in materials?

The Fermi-sphere and band structure are closely related, as they both describe the energy levels and behavior of electrons in a material. The Fermi-sphere is used to determine the occupancy of energy levels, while band structure describes the allowed energy states for electrons in a material.

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