# Coulomb potential removes the degnerecay of states

1. Feb 20, 2009

### eman2009

Hi every one this is the first time in this wonderful forum :)

and i have a question i hope i find an answer ????

how can the additiona of a smalll (c/r square)term to the coulomb potential removes the degnerecay of states with different (small) L. (quantum defect)?

thanks

2. Feb 21, 2009

### malawi_glenn

Re: degeneracy

Do you want a full mathematical calculation or a quantitative answer?

3. Feb 21, 2009

### eman2009

Re: degeneracy

__________________

4. Feb 21, 2009

### malawi_glenn

Re: degeneracy

do you know perturbation theory?

5. Feb 21, 2009

### eman2009

Re: degeneracy

yes how i can use it in this case??????

6. Feb 21, 2009

### malawi_glenn

Re: degeneracy

generally, a perturbation lifts the degeneracy.

The additional factor 1/r^2 is related to the spin-orbit interaction, which will have a 1/r^2 dependence $$\frac{1}{r}\frac{dV_C}{dr}(vec{L}\cdot \vec{S})$$ The derivative of the couloumb potential is 1/r^2 and L is proportional to r

7. Feb 21, 2009

### jamesmaxwell

Re: degeneracy

I suggest that you refer to text book.
(For example, Griffiths chapter 6)

By using perturbation theory, you can calculate aproximate energy and fine slit of energy level on same value of L^2.

<1/r^2> can be calculated and it's value contains n,l so you may take good quantum number n,l ...

8. Feb 21, 2009

### eman2009

Re: degeneracy

thanks for all :)