- #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

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?