By inverse Fourier-Laplace transform, the potential due to each particle is the sum of two parts One corresponds to the excitation of Langmuir waves by the particle, and the other one is its screened potential, as classically obtained by a linearized Vlasovian calculation involving a test particle. The screened potential is the above screened Coulomb potential for a thermal plasma and a thermal particle. For a faster particle, the potential is modified. Substituting an integral over a smooth distribution function for the discrete sum over the particles in S ( k , ω ω ) , yields the Vlasovian expression enabling the calculation of Landau damping.