Condensed Matter Physics - Fermi velocity, etc.

Graham87
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Homework Statement
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Relevant Equations
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1.png

I have made solutions a-d, but my fermi velocity seems too big.
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Have you used Ef= 5 J?
Remember, it's Ef= 5 eV.
 
Gordianus said:
Have you used Ef= 5 J?
Remember, it's Ef= 5 eV.
Thanks! I realized that later. When I converted eV to joule I got the right Fermi velocity.

However, how may I got mean electron speed?
I know that most of the electrons are not on the Fermi surface, and I need to find the mean speed of all electrons.
 
Do you know something about the density of states function g(E)?
 
Gordianus said:
Do you know something about the density of states function g(E)?
We know that density of states in 2D is (L/2pi)^2 ?
So DOS is the no of electrons per unit area? So I just have to multiply DOS with unit area to find the total electrons?
But I will need the velocity of the total electrons?
 
Last edited:
I think I solved most of my problem now.

However I’m not 100% sure about mean speed in a). I used the formula and plugged in Fermi energy there, but might there be another E that should be there instead?

Thanks
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Thread 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
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Thread 'Number of quantum accessible states of a particle given T, N?'

It's given a gas of particles all identical which has T fixed and spin S. Let's ##g(\epsilon)## the density of orbital states and ##g(\epsilon) = g_0## for ##\forall \epsilon \in [\epsilon_0, \epsilon_1]##, zero otherwise. How to compute the number of accessible quantum states of one particle? This is my attempt, and I suspect that is not good. Let S=0 and then bosons in a system. Simply, if we have the density of orbitals we have to integrate ##g(\epsilon)## and we have...
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