  For quantum mechanics on a lattice the position (``particle number'')
operator and the quasi-momentum (``phase'') operator obey canonical commutation
relations (CCR) only on a dense set of the Hilbert space. We compare exact
numerical results for a particle in simple potentials on the lattice with the
expectations, when the CCR are assumed to be strictly obeyed. Only for
sufficiently smooth eigenfunctions this leads to reasonable results. In the
long time limit the use of the CCR can lead to a qualitativel wrong dynamics
even if the initial state is in the dense set.
