  The acceleration theorem for Bloch electrons in a homogenous external field
is usually presented using quasiclassical arguments. In quantum mechanical
versions the Heisenberg equations of motion for an operator $\hat {\vec k}(t)$
are presented mostly without properly defining this operator. This leads to the
surprising fact that the generally accepted version of the theorem is incorrect
for the most natural definition of $\hat {\vec k}$. This operator is shown not
to obey canonical commutation relations with the position operator. A similar
result is shown for the phase operators defined via the Klein factors which
take care of the change of particle number in the bosonization of the field
operator in the description of interacting fermions in one dimension. The phase
operators are also shown not to obey canonical commutation relations with the
corresponding particle number operators. Implications of this fact are
discussed for Tomonaga-Luttinger type models.
