- #1

leoneri

- 19

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1. I am reading the book 'Solid State Physics', 1976, by Aschcroft and Mermin. I am reading chapter II about 'The Sommerfeld Theory of Metals'. (I hope anyone here have the same book..)

I found it hard to figure out one integral on the equation (2.30) on calculation of the 3D electron gas energy density 'E/V' when putting limit V -> infinity.

My question is why the integration (1/(4*Pi^3)) * integral(dk * (h_bar^2*k^2)/(2*m)) is equal to (1/Pi^2) * (h_bar^2*k_Fermi^5)/(10*m) ? I have tried it but I know that integration of k^2 is (1/3)*k^3, so I don't get it on how to get the result...

Sorry that I do not know LaTex..

2. I read on wikipedia. They calculate the total energy by doing integration of Fermi energy over N, which is the total number of electron. My question is, why is it like that? As far as know, not all electrons sit in the same energy level equal to Energy Fermi due to Pauli principle. So it does not make sense to me while the result is correct the the total energy is equal to 3/5 of Energy Fermi times the number of electron. Can anybody here explain it? Source: http://en.wikipedia.org/wiki/Fermi_energy#The_three-dimensional_case

Many Thanks in advance.