Time-dep perturbation theory

[omyojj]

while I`m reading the griffiths` textbook..

got my curiosity from "Typically, the diagonal matrix elements of H` vanish"

i.e. <a|H`|a>=0 in general..

If V(x) does not have an angular dependence..

the selection rule implies <a|H`|a>=0 (since Δl=0)..yes..

but what if it does?

what it(vanishing diagonal element of H`) means
physically (in view of the perturbation theory)

sorry for my bad english..

 

[Dr Transport]

If the diagonal elements of the perturbation didn't vanish, then they wouldn't perturb the system but be a small addtion to the unperturbed eigenvalue or another eigenstate.