- #1
kelly0303
- 561
- 33
Hello! I found an expression in this paper (eq. 1) for the multipole expansion of the vector potential. I am not sure I understand what form do the vector spherical harmonics (VSH) have. Also, for example, the usual hyperfine interaction operator is given by ##\frac{\mathbf{\mu}\cdot(\mathbf{r}\times \mathbf{\alpha})}{r^3}##. I am not sure how to get back to this expression using equation 1 (or 2), for k=1. On Wikipedia it seems like VSH are defined as ##Y_{lm}\hat{r}##, while in the reference they mention in the paper it would be ##\frac{1}{\sqrt{J(J+1)}}\mathbf{L}Y_{JM}##, where ##\mathbf{L}## is the orbital angular momentum operator. I tried using both and still didn't get back the original formula. Can someone help me with this? Thank you!