Thanks for the reply.
I am guessing the first point is due to exchange symmetry? I am not sure how to visualise this... is there a mathematical proof to this?
Hi!
I saw something on my lecture notes that I don't really understand. It reads "Rare gases have filled s and p-sub-shells, which leads to a spherically symmetric charge distribution. Since electrons are indistinguishable they take on a common wavefunction. The point is that this results in a...
Ok I see you what you mean, but how could I evaluate the matrix elements <nlm_l'sm_s'|\hat{S}\cdot\hat{L}|nlm_lsm_s> if I cannot use the eigenvalue equation?
Hiya! Thanks for the reply!
I think my thought process went like this:
Suppose I have an operator \hat{Q} , then the eigenvalue equation \hat{Q} |q>=q|q> can only be evaluated if |q> is an eigenstate of \hat{Q} .
Then since |nlm_lsm_s> is not an eigenstate of \hat{S}\cdot\hat{L} , then...
Hello! This is my first time posting, so please correct me if I have done anything incorrectly.
There's something that I don't understand about the spin-orbit interaction.
First of all I know that
[\hat{S} \cdot \hat{L}, \hat{L_z}] \ne 0
[\hat{S} \cdot \hat{L}, \hat{S_z}] \ne 0
so this means...