  We show that Bohr's principle of complementarity between position and
momentum descriptions can be formulated rigorously as a claim about the
existence of representations of the CCRs. In particular, in any representation
where the position operator has eigenstates, there is no momentum operator, and
vice versa. Equivalently, if there are nonzero projections corresponding to
sharp position values, all spectral projections of the momentum operator map
onto the zero element.
