  We revisit Wigner's question about the admissible commutation relations for
coordinate and velocity operators given their equations of motion (EOM). In
more general terms we want to consider the question of how to quantize
dynamically equivalent Hamiltonian structures. A unique answer can presumably
be given in those cases, where we have a dynamical symmetry. In this case
arbitrary deformations of the symmetry algebra should be dynamically
equivalent. We illustrate this for the linear as well as the singular
1d-oscillator. In the case of nonlinear EOM quantum corrections have to be
taken into account. We present some examples thereof New phenomena arise in
case of more then one degree of freedom, where sometimes the interaction can be
described either by the Hamiltonian or by nonstandard commutation relations.
This may induce a noncommutative geometry (for example the 2d-oscillator in a
constant magnetic field). Also some related results from nonrelativistic
quantum field theory applied to solid state physics are briefly discussed
within this framework
