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

by kamaln
Tags: energy, fermions, ground, state
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Oct24-10, 03:28 PM
P: 1
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

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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