- #1
Nixom
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In many textbooks, the non-commutativity for the canonical pair is considered to lead to the major variaty from classical mechanism(CM) to quantum mechanism(QM), and change the Possion bracket into quantum commutator is a standard procedure called as canonical quantization. But in fact the Possion bracket of x and p in classical mechanism are also non-vanishing. In my opinion both the QM and CM have the same algebraic structure, they ought not to appear much different in formalism, but they do indeed, why?