Editing Quantization (physics) (section)

== Quantization schemes ==
Even within the setting of canonical quantization, there is difficulty associated to quantizing arbitrary observables on the classical phase space. This is the '''ordering ambiguity''': classically, the position and momentum variables ''x'' and ''p'' commute, but their quantum mechanical operator counterparts do not. Various ''quantization schemes'' have been proposed to resolve this ambiguity,<ref>{{harvnb|Hall|2013}} Chapter 13</ref> of which the most popular is the [[Wigner–Weyl transform|Weyl quantization scheme]]. Nevertheless, [[Canonical quantization#Groenewold.27s theorem|Groenewold's theorem]] dictates that no perfect quantization scheme exists. Specifically, if the quantizations of ''x'' and  ''p''  are taken to be the usual position and momentum operators, then no quantization scheme can perfectly reproduce the Poisson bracket relations among the classical observables.<ref>{{harvnb|Hall|2013}} Theorem 13.13</ref>