where V (⃗ z ′ ) is perturbing potential at point ⃗ z ′ . In other words, the Lindhard function χ0(⃗ x, ⃗ z ′ ) tells us how perturbation at point ⃗ z ′ affects the electrons at point ⃗ x (and vice versa). Then we sum over all possible points ⃗ z ′ , and we obtain in the end the total contribution towards charge density at point ⃗ x.