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I am new here, and also new to quantum mechanics. This is the question to which I can't answer neither in mathematical nor physical way.

a,b → observables (like position and momentum)

A,B → corresponding operators.

"It is possible for particles to be in a state of definite a and b at the same time only if the corresponding operators A and B commute."

Why?

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# Simultaneous measuring of two operators

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