Undergrad HUP in condensates?

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SUMMARY

The discussion centers on the position-momentum commutators of independent photons, specifically [x1,p1] and [x2,p2], both equal to ih/2π, while [x1,p2] and [x2,p1] equal 0 due to their independence. However, the question arises regarding the validity of these commutators when the photons are in the same quantum state or part of a condensate. The consensus is that the commutator relationships remain valid across all states, emphasizing that the significance of quantum mechanics lies in the complexity of quantum states rather than the commutators themselves.

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TL;DR
Position-momentum commutators for particles in a condensate
Given two independent photons. The position-momentum commutator for particle 1, [x1,p1] is ih/2π and the commutator for particle 2 , [x2,p2] is also ih/2π. Also, [x1,p2] = 0 and [x2,p1] = 0 because the 2 photons are independent.

But what if the two photons are in the same quantum state or part of a condensate? Is it still true that [x1,p2] = 0 and [x2,p1] = 0?

Thanks in advance.
 
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It's always true, the commutator expresses something which is valid for all states. The true magic of quantum mechanics is not so much in the nontrivial commutators as it is in nontrivial quantum states.
 

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