  Based on the vanishing of the second Hochschild cohomology group of the
enveloping algebra of the Heisenberg algebra it is shown that differential
algebras coming from quantum groups do not provide a non-trivial deformation of
quantum mechanics. For the case of a q-oscillator there exists a deforming map
to the classical algebra. It is shown that the differential calculus on quantum
planes with involution, i.e. if one works in position-momentum realization, can
be mapped on a q-difference calculus on a commutative real space. Although this
calculus leads to an interesting discretization it is proved that it can be
realized by generators of the undeformed algebra and does not posess a proper
group of global transformations.
