This integration must be split into two due to the absolute value | z − − z ′ | inside the integrand. The regions are z < 0 and z > 0 . Again, a convergence factor must be introduced to evaluate both integrals and the result is π π e , p ( z , t ) = − − P e − − i ω ω t 2 ϵ ϵ 0 k 0 { 1 k + k 0 e − − i k 0 z z < 0 2 k 0 k 0 2 − − k 2 e i k z + 1 k − − k 0 e i k 0 z z > 0.