Undergrad HUP in condensates?

[LarryS]

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.

 

[Demystifier]

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.