where the factor Ω d r d-1 comes from the differential volume form dV = Ω d r d-1 dr, Dirac delta satisfies (from the definition) δ (d) (⃗ r) = Ω d r d-1 δ(r), and we used the radial term for the Laplacian in d dimensions. In the region where r > 0 and the Dirac delta is zero, we obtain instead