Compatible observables and commutator

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Thread starter Haynes Kwon
Start date Nov 11, 2019
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Commutator observables

In summary, compatible observables are physical quantities that can be measured simultaneously with precise values and their corresponding operators commute. The commutator of two observables is a mathematical operation that determines whether their operators commute or not. If two observables are compatible, it allows for more accurate measurements and reduces uncertainty. However, if two observables do not commute, it leads to uncertainty and can affect the accuracy of the measurements. Compatible observables play a crucial role in quantum mechanics as they relate to the uncertainty principle and the commutation of their corresponding operators.

Nov 11, 2019

Haynes Kwon

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Is commutator being zero for two operators the same statement as the two observables are compatible?

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Nov 11, 2019

PeroK

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Haynes Kwon said:

Is commutator being zero for two operators the same statement that the two observables are compatible?

Yes.

Related to Compatible observables and commutator

1. What are compatible observables?

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.

2. What is the commutator of two observables?

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.

3. What is the significance of compatible observables?

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.

4. Can all observables be measured simultaneously?

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.

5. How do compatible observables affect the uncertainty principle?

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.