The spreading of wave packets in quantum mechanics is directly related to the spreading of probability densities in diffusion. For a particle which is randomly walking, the probability density function at any point satisfies the diffusion equation (also see the heat equation), ∂ ∂ ∂ ∂ t ρ ρ = 1 2 ∂ ∂ 2 ∂ ∂ x 2 ρ ρ , where the factor of 2, which can be removed by rescaling either time or space, is only for convenience.