To see this, note that the integral over all space of K equals 1 at all times, ∫ ∫ K t ( x ) d x = 1 , since this integral is the inner-product of K with the uniform wave function. But the phase factor in the exponent has a nonzero spatial derivative everywhere except at the origin, and so when the time is small there are fast phase cancellations at all but one point. This is rigorously true when the limit ε →0 is taken at the very end.