# Central Potential Problem

1. May 21, 2005

### truth_hunter

How can I calculate the AM and energy of each level in a resulting multiplet of a particle of spin=1/2 with orbital AM quantum number, L=2 subject to a spin orbit potential,
V=lamda(L.S)?
i am at my wits end!

2. May 21, 2005

### dextercioby

Well,technically

$$\hat{\vec{J}}=\hat{\vec{L}}+\hat{\vec{S}}$$

Use the C-G theorem to generate the irreducible spaces and the C-G formula to find the basis in such spaces.
Then,once u got the basis,then,using perturbation theory for a nondegenerate energy level

$$\Delta E^{(1)} =\langle n,j,m_{j} |\hat{V}|n,j,m_{j}\rangle$$

Daniel.

3. May 21, 2005

### truth_hunter

Cheers mate, I can do it now.
Thanks