The commutator of two operators A and B, which measures the degree of incompatibility between A and B, is AB - BA (at least according to one textbook I have). But multiplying/substracting matrices just yields matrices! (http://en.wikipedia.org/wiki/Matrix_multiplication).(adsbygoogle = window.adsbygoogle || []).push({});

So firstly, how can a matrix measure incompatibility?

Secondly, how can this equation be valid if the commutator of position and momentum is a number i times h-bar?

Thirdly, how is a weird number like i times h-bar a measure of anything?

Very confused, please help.

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# Commutators; matrices? numbers? both?

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