3 votes

The question about commutator $[\hat{x},\hat{p}]=i\hbar$ at $\hbar\rightarrow 0$ seemingly can't match with Poisson bracket $\{x,\,p\}=1$

There is a systematic invertible change of language (Weyl correspondence) between Hilbert space operators and phase-space q-number variables, $$ \hat A \leftrightarrow A, \qquad \hat B \leftrightarrow ...
Cosmas Zachos's user avatar
2 votes

The question about commutator $[\hat{x},\hat{p}]=i\hbar$ at $\hbar\rightarrow 0$ seemingly can't match with Poisson bracket $\{x,\,p\}=1$

Well... $[x,p]=0$ for classical variables so there's no formal problem there. The simplest quantization procedure is due to Dirac in his classic P.A.M.Dirac, The Principles of Quantum Mechanics ...
ZeroTheHero's user avatar
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