My recollection is that in nonrelativistic N-particle QM you would have a wavefunction ψ(r1,r2,…,rN) (a complex number for every possible choice of N positions in space for the N particles), and when you change gauge you multiply that that wavefunction by eiq1Λ(r1)/ℏeiq2Λ(r2)/ℏ⋯eiqNΛ(rN)/ℏ. I think this is equivalent to what Vanessa said, and if not she’s probably right :-P
That was my original guess! I think Vanessa suggested something different. IIUC, she suggested
ψ(r1,r2,…,rN)↦N∏k=1(eiqkΛ(rk)/ℏψ(r1,r2,…,rN))
which has N factors of the wavefunction, instead of 1.
(You having the same guess as me does update me towards the hypothesis that Vanessa just forgot some parentheses, and now I’m uncertain again :-p. Having N factors of the wavefunction sure does seem pretty wacky!)
(...or perhaps there’s an even more embarassing misunderstanding, where I’ve misunderstood physicist norms about parenthesis-insertion!)
I think it’s just one copy of the ψ—I don’t think Vanessa intended for ψ to be included in the Π product thing here. I agree that an extra pair of parentheses could have made it clearer. (Hope I’m not putting words in her mouth.)
My recollection is that in nonrelativistic N-particle QM you would have a wavefunction ψ(r1,r2,…,rN) (a complex number for every possible choice of N positions in space for the N particles), and when you change gauge you multiply that that wavefunction by eiq1Λ(r1)/ℏeiq2Λ(r2)/ℏ⋯eiqNΛ(rN)/ℏ. I think this is equivalent to what Vanessa said, and if not she’s probably right :-P
That was my original guess! I think Vanessa suggested something different. IIUC, she suggested
ψ(r1,r2,…,rN)↦N∏k=1(eiqkΛ(rk)/ℏψ(r1,r2,…,rN))
which has N factors of the wavefunction, instead of 1.
(You having the same guess as me does update me towards the hypothesis that Vanessa just forgot some parentheses, and now I’m uncertain again :-p. Having N factors of the wavefunction sure does seem pretty wacky!)
(...or perhaps there’s an even more embarassing misunderstanding, where I’ve misunderstood physicist norms about parenthesis-insertion!)
I think it’s just one copy of the ψ—I don’t think Vanessa intended for ψ to be included in the Π product thing here. I agree that an extra pair of parentheses could have made it clearer. (Hope I’m not putting words in her mouth.)