• Starting from the general expression for the Green’s function for a homogeneous system, Gαβ(k,ω), derive the formula for the Green’s function in the non-interacting system, G0αβ(k,ω).
• Starting from the general expressions for obtaining the expectation value of any single-particle operator and the ground-state energy of a system from the Green’s function, derive the expectation value of the totalnumber operator <N and the total energy E0 for the non-interacting system of electrons.
