What does it mean that classical operators commute?
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The physical significance in quantum mechanics follows from the generalised uncertainty principle, which relates the product of the standard deviations of two measurements to the value of the commutator. The key is to note that, because of this, if the commutator is zero, the two standard deviations are essentially independent of each other.
The physical significance in quantum mechanics follows from the generalised uncertainty principle, which relates the product of the standard deviations of two measurements to the value of the commutator. The key is to note that, because of this, if the commutator is zero, the two standard deviations are essentially independent of each other.
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