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pythagoras88
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Hi,
Just wondering, can we prove that there is a maximal complete set of commuting observable?
Just wondering, can we prove that there is a maximal complete set of commuting observable?
In the cases of interest, it is easy to write one such set down, based on the way the Hilbert space is defined.pythagoras88 said:Hi,
Just wondering, can we prove that there is a maximal complete set of commuting observable?
pythagoras88 said:Do you know of any reference that has the proof for extending every set to a maximal set? Or is this kind of like a trivial fact that does not require much proving?
A maximal complete set of commuting refers to a group of physical quantities in a quantum mechanical system that can be measured simultaneously without affecting each other. These quantities are known as commuting observables, and their corresponding operators can be simultaneously diagonalized, leading to a complete set of compatible eigenstates.
There is no direct way to prove the existence of a maximal complete set of commuting. However, it can be inferred from the Heisenberg uncertainty principle, which states that certain pairs of observables cannot be measured simultaneously with arbitrary precision. Therefore, if a set of observables can be measured without violating the uncertainty principle, it can be considered a maximal complete set of commuting.
Yes, there are several real-world applications of a maximal complete set of commuting. One example is in quantum information processing, where a complete set of commuting observables is used to encode and manipulate quantum states. It is also essential in quantum mechanics to accurately describe and predict the behavior of physical systems.
Yes, a maximal complete set of commuting can change over time. This is because in quantum mechanics, the values of observables can change with time due to the system's evolution. As a result, the set of commuting observables can also change over time.
No, it is not possible to prove the existence of a maximal complete set of commuting experimentally. However, its existence can be supported by experimental evidence, such as observing the simultaneous measurement of compatible observables without violating the uncertainty principle. This provides indirect evidence for the existence of a maximal complete set of commuting in a physical system.