Returning to one dimension for simplicity, with m and ħ set equal to one, when a is the infinitesimal quantity ε, the Gaussian initial condition, rescaled so that its integral is one, ψ ψ 0 ( x ) = 1 2 π π ε ε e − − x 2 2 ε ε becomes a delta function, δ (x), so that its time evolution, K t ( x ) = 1 2 π π ( i t + ε ε ) e − − x 2 2 i t + ε ε yields the propagator.