- #1
aliens123
- 75
- 5
I am attaching an image from David J. Griffith's "Introduction to Quantum Mechanics; Second Edition" page 205.
In the scenario described (the Hamiltonian treats the two particles identically) it follows that
$$PH = H, HP = H$$
and so $$HP=PH.$$
My question is: what are the necessary and sufficient conditions to have that $$[P,H]=0?$$ Clearly
$$PH = H, HP = H$$
is sufficient, but is it necessary?
Also, as a bonus question, because the exchange operator is an observable, what would it mean to "measure" this in a laboratory?
In the scenario described (the Hamiltonian treats the two particles identically) it follows that
$$PH = H, HP = H$$
and so $$HP=PH.$$
My question is: what are the necessary and sufficient conditions to have that $$[P,H]=0?$$ Clearly
$$PH = H, HP = H$$
is sufficient, but is it necessary?
Also, as a bonus question, because the exchange operator is an observable, what would it mean to "measure" this in a laboratory?