Observable - Incompatibility of Observables in Quantum Mechanics

Incompatibility of Observables in Quantum Mechanics

A crucial difference between classical quantities and quantum mechanical observables is that the latter may not be simultaneously measurable. This is mathematically expressed by non-commutativity of the corresponding operators, to the effect that

This inequality expresses a dependence of measurement results on the order in which measurements of observables and are performed. Observables corresponding to non-commutative operators are called incompatible.

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