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Dec 19, 2017 at 15:29 vote accept proton
Dec 19, 2017 at 3:07 comment added Matthew Titsworth No. The implication is that if I take $\lambda_2$ and then $\lambda_2^{-1}$ I get the identity.
Dec 18, 2017 at 20:51 comment added proton In the last paragraph, don't you imply that $\lambda_2^{-1}=1$?
Dec 18, 2017 at 6:22 comment added Matthew Titsworth 1. Yes, though in this case the appropriate question is to ask "can the exchange be implemented adiabatically?" Quantum mechanics is built off of the Hamiltonian and Lagrangian formalisms and so really we're interested in the energetics. Bringing up conservative forces was to provide a foot hold on the explanation for path independence. 2. I've provided an explanation which addresses this in the new 3rd- and 2nd to last paragraphs.
Dec 18, 2017 at 6:20 history edited Matthew Titsworth CC BY-SA 3.0
And 3rd and 2nd to last paragraphs to address question in comments.
Dec 17, 2017 at 8:10 comment added proton Thank! I have two questions: 1. Is it possible to implement the exchange in the lab using only conservative forces? 2. Regarding the last paragraph, why is going backward on path $\lambda_2$ not like going forwards?
Dec 17, 2017 at 5:52 history answered Matthew Titsworth CC BY-SA 3.0