  A proof is given that an invertible and a unitary operator can be used to
reproduce the effect of a q-deformed commutator of annihilation and creation
operators. In other words, the original annihilation and creation operators are
mapped into new operators, not conjugate to each other, whose standard
commutator equals the identity plus a correction proportional to the original
number operator. The consistency condition for the existence of this new set of
operators is derived, by exploiting the Stone theorem on 1-parameter unitary
groups. The above scheme leads to modified equations of motion which do not
preserve the properties of the original first-order set for annihilation and
creation operators. Their relation with commutation relations is also studied.
