- #1
Wminus
- 173
- 29
Hi!
If I have understood things correctly, in a multi-electron atom you have that the spin operator ##S## commutes with the orbital angular momentum operator ##L##. However, as these operators act on wavefunctions living in different Hilbert spaces, how is it possible to even calculate the commutator?
I mean, you can't calculate the commutator between ##\hat{H} = i \hbar \frac{\partial}{\partial t}## and ##\hat{p}= \frac{\hbar}{i} \vec{\nabla}## precisely because of different hiblert spaces, so why is ##L## and ##S## different?
If I have understood things correctly, in a multi-electron atom you have that the spin operator ##S## commutes with the orbital angular momentum operator ##L##. However, as these operators act on wavefunctions living in different Hilbert spaces, how is it possible to even calculate the commutator?
I mean, you can't calculate the commutator between ##\hat{H} = i \hbar \frac{\partial}{\partial t}## and ##\hat{p}= \frac{\hbar}{i} \vec{\nabla}## precisely because of different hiblert spaces, so why is ##L## and ##S## different?