Hello everybody, I just have no idea how to start this problem so i was hoping you guys would point me in the right direction and then i'll be able to go on by myself(adsbygoogle = window.adsbygoogle || []).push({});

the problem asks to show that the total ground state energy of N fermions in a three dimensional box is given by E total = 3/5*N*(E fermi)

some relevant equations to this are:

D(E)dE=2(1/8)4pi*r^2 dr

N=[V(2m(E fermi))^(3/2)] / [3*(hbar^3)pi^2]

E fermi = [(hbar^2)/2m]*[(3pi^2*N)/V]^2/3

I don't have any attempt at a solution because i don't know how to begin proving that E total = 3/5*N*(E fermi). Thanks in advance for any help that I get.

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# Total ground state energy of N fermions in a 3D box

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