3. Prove that the Hartree-Fock contribution to the energy of the

3. Prove that the Hartree-Fock contribution to the energy of the state of momentum k in a uniform electron gas is given by Eq. (1.34). eAln-ti VINT(r, N) [1.47] - r,| 4. Use the screened interaction of Eq. (1.47) to calculate the screened exchange energy of the lowest (k = 0) state of a uniform electron gas and compare this with the Thomas-Fermi correlation hole contribution in the limits of low and high electron density. ekp (k k) In |k; + k E(k) = 2m [1.34] kk