# Coulomb potential removes the degnerecay of states

• eman2009
In summary, the conversation discusses the addition of a small (1/r^2) term to the Coulomb potential in order to remove the degeneracy of states with different (small) quantum defects. The use of perturbation theory is suggested, as it can approximate the energy and fine structure of energy levels with the same value of L^2. The value of <1/r^2> can be calculated, and it depends on the good quantum numbers n and l. Textbook references, such as Griffiths chapter 6, are recommended for further understanding.
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

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

__________________

do you know perturbation theory?

yes how i can use it in this case?

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

I suggest that you refer to textbook.
(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 ...

thanks for all :)

## 1. What is Coulomb potential?

Coulomb potential is a type of electrostatic potential energy that arises from the interaction between charged particles.

## 2. How does Coulomb potential remove the degeneracy of states?

Coulomb potential removes the degeneracy of states by creating an energy barrier that prevents electrons from occupying the same energy level. This allows for more distinct energy levels and reduces the chance of two electrons having the same set of quantum numbers.

## 3. What is degeneracy of states?

Degeneracy of states refers to the phenomenon in which two or more quantum states have the same energy level.

## 4. Why is the degeneracy of states problematic in quantum systems?

The degeneracy of states can lead to confusion and difficulty in accurately describing and predicting the behavior of quantum systems. It also violates the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state.

## 5. How is Coulomb potential related to the stability of atoms?

Coulomb potential plays a crucial role in determining the stability of atoms. It helps to maintain the distinct energy levels of electrons, preventing them from collapsing into the nucleus and stabilizing the atom.

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