Posted by Steve Simon on March 27, 2014, 7:25 pm, in reply to "2013 paper question 2"
Yes, I see your trouble with this question. There certainly seems to be a bit of an inconsistency. Let me try to rephrase what the question is trying to say. When you consider interacting electrons the Hamiltonian has two parts, a kinetic energy term, the usual hbar^2 k^2/2m, and an interaciton part, V(r_i  r_j). You would like to calculate the total energy ofthe whole system, and it is tempting to calculate the two pieces seperately. In the approximation that the quesiton wants you to use, to calculate the kinetic energy, you fill a fermi sea with momenta k < k_F, and you sum the kinetic energy of each state. So you would write E_kinetic = sum_{k 
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