- #1

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[tex]

E = 2 \int_0^{k_f} \frac{\hbar^2 k^2}{2m} 3k^2 dk

[/tex]

Where the factor of two is due to the fact that there are two electron states for each value of k. The idea is to add up all the energies of all states within the fermi sphere, but it does not give the correct result which is:

[tex]

E = \frac{3}{5} N k_f

[/tex]

Where N is the number of electrons, and [tex]k_f[/tex] is the radius of the fermi sphere. What am I doing wrong? If you need more info please let me know.

Thanks in advance

René