The wave that emerges from a point source has amplitude ψ ψ at location r that is given by the solution of the frequency domain wave equation for a point source (the Helmholtz equation), ∇ ∇ 2 ψ ψ + k 2 ψ ψ = δ δ ( r ) , where δ δ ( r ) is the 3-dimensional delta function. The delta function has only radial dependence, so the Laplace operator (a.k.a. scalar Laplacian) in the spherical coordinate system simplifies to ∇ ∇ 2 ψ ψ = 1 r ∂ ∂ 2 ∂ ∂ r 2 ( r ψ ψ ) .