Can someone explain to me why the ground state energy of a free electron fermi gas is not just:(adsbygoogle = window.adsbygoogle || []).push({});

[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

RenĂ©

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Ground state energy of free electron fermi gas

**Physics Forums | Science Articles, Homework Help, Discussion**