A mathematical formulation of the famous Heisenberg uncertainty principle is that a certain pair of linear transformations P and Q satisfies, after suitable normalizations, the equation PQ - QP = 1. It is easy enough to produce a concrete example of this behavior; consider L2(-∞, +∞) and let P and Q be the differentiation transformation and the position transformation, respectively (that is, (Pf) (x) = f’(x) and (Qf) (x) = xf(x)). These are not bounded linear transformations, of course, their domains are far from being the whole space, and they misbehave in many other ways. Can this misbehavior be avoided?