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Cohen-Tannoudji has this section in his quantum mechanics book where he derives a bunch of relations which are true for operators having the commutation relation [itex][Q,P]=i\hbar[/itex]. Is there any special significance to this value of a commutator? Would things be much different if it had the value 1 ?

Also, if we have two sets of operators with the same commutator, i.e. [itex][x,p]=[Q,P]=i\hbar[/itex], what does this tell us about the relations between the operators, if anything?