Recent content by PhysicsKin

Is there a quick way to show that it is not diagonal?

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...