Following Dirac [1], the rules of canonical quantization include classical and quantum contact transformations of classical and quan- tum phase space variables. While arbitrary classical canonical coor- dinate transformations exist that is not the case for some analogous quantum canonical coordinate transformations. This failure is due to the rigid connection of quantum variables arising by promoting the corresponding classical variable from a c-number to a q-number. A different relationship of c-numbers and q-numbers in the procedures of Enhanced Quantization [2] shows the compatibility of all quantum operators with all classical canonical coordinate transformations.
John Rider Klauder