for some complex numbers a , b , c with Re ⁡ ⁡ ( a ) > 0 (Hudson's theorem). Note that a is allowed to be complex, so that ψ ψ is not necessarily a Gaussian wave packet in the usual sense. Thus, pure states with non-negative Wigner functions are not necessarily minimum-uncertainty states in the sense of the Heisenberg uncertainty formula ; rather, they give equality in the Schrödinger uncertainty formula, which includes an anticommutator term in addition to the commutator term. (With careful definition of the respective variances, all pure-state Wigner functions lead to Heisenberg's inequality all the same.)