Coulomb potential removes the degnerecay of states

[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

 

[malawi_glenn]

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

 

[eman2009]

no just quantitative answer?
__________________

 

[malawi_glenn]

do you know perturbation theory?

 

[eman2009]

yes how i can use it in this case?

 

[malawi_glenn]

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

 

[jamesmaxwell]

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

By using perturbation theory, you can calculate approximate 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 ...

 

[eman2009]

thanks for all :)