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This is for classical mechanics. If we write commutation relation, for instance, for location and momentum, we obtain Heisenberg uncertainty relation.

But, what is a pedagogical transfer from Poisson bracket to quantum mechanics. Because formulae are very different, Classical one has partial derivations, quantum one has only multiplication of matrices.

What is transfer to quantum mechanics, or in the opposite direction?

One example of this question:

http://physics.stackexchange.com/questions/19770/what-is-the-connection-between-poisson-brackets-and-commutators

But; i think, that it can be answered more clearly.