By contrast, as an example of dispersion where a wave changes shape during propagation, consider instead solutions to the free Schrödinger equation (nondimensionalized with 2Δ x, m, and ħ set equal to one), i ∂ ∂ ψ ψ ∂ ∂ t = − − 1 2 ∇ ∇ 2 ψ ψ , yielding the dispersion relation ω ω = 1 2 | k | 2 .