Physical meaning of a commutator?

[Fellowroot]

I know how to use a commutator as a mathematical formula but I really don't understand what it means. Can anyone explain it to me.

Is a commutator nothing more than a check to see if it commutes or not since I know that if you use a commutator with a wave function and the result equals zero then you can have a definite value for the observables (operators) simultaneously?



Thanks.

 

[M Quack]

https://www.physicsforums.com/showthread.php?t=131975

If two operators do not commute, then they cannot be measured simultaneously with infinite precision - the pair of observables has to obey Heisenberg's uncertainty principle.

If an operator commutes with the Hamiltonian, then its expectation value is constant.