- #1

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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?

- Thread starter pythagoras88
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- #1

- 17

- 0

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?

- #2

A. Neumaier

Science Advisor

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In the cases of interest, it is easy to write one such set down, based on the way the Hilbert space is defined.Hi,

Just wondering, can we prove that there is a maximal complete set of commuting observable?

On the other hand, proving that every set of commuting observables on every Hilbert space can be extended to a maximal such set probably requires the axiom of choice.

- #3

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Thanks for the reply.

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?

- #4

A. Neumaier

Science Advisor

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Given some such set S, if it is not maximal, you can (by definition of maximality) add another operator to get a bigger set. Now apply the Lemma of Zorn (which is equivalent to the axiom of choice).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?

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