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Haynes Kwon
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Is commutator being zero for two operators the same statement as the two observables are compatible?
Haynes Kwon said:Is commutator being zero for two operators the same statement that the two observables are compatible?
Compatible observables refer to physical quantities that can be measured simultaneously and have well-defined values at the same time. This means that the observables commute with each other, meaning their order of measurement does not affect the outcome.
The commutator of two observables is a mathematical operation that determines whether the two observables are compatible or not. It is defined as the difference between the product of the two observables measured in different orders.
Compatible observables have a significant role in quantum mechanics as they represent physical quantities that can be measured simultaneously with precise values. This allows for a more accurate and complete understanding of a system's state.
No, not all observables can be measured simultaneously. Only compatible observables can be measured simultaneously with precise values. Incompatible observables will have uncertain values when measured together.
Compatible observables have a special relationship with the uncertainty principle. If two observables are compatible, their uncertainties will be inversely proportional, meaning that the more precisely one observable is measured, the less precisely the other can be measured.