LS-coupling for configurations with equivalent electrons

In summary, the values of the magnetic quantum numbers ml1, ml2, ms1, and ms2 for two electrons in a np2 configuration are -1, 0, 1 for ml and -1/2, 1/2 for ms. By combining these values and taking into account antisymmetric states, it can be shown that there are fifteen degenerate states within the central field approximation. This is achieved by combining the two l=1 states and two s=1/2 states to get the total orbital angular momentum and spin, respectively. Only antisymmetric states are included in this calculation.
  • #1
damaks
2
0
List the values of the magnetic quantum numbers ml1, ml2
ms1 and ms2 for the two electrons in a np2 configuration to show that fifteen degenarate states exists within the central field approximation.

ml can take values -1,0,1 i believe.
ms can take values -1/2 and 1/2.

how does this ad up to fifteen degenarate states?
 
Last edited:
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  • #2
damaks said:
List the values of the magnetic quantum numbers ml1, ml2
ms1 and ms2 for the two electrons in a np2 configuration to show that fifteen degenarate states exists within the central field approximation.

ml can take values -1,0,1 i believe.
ms can take values -1/2 and 1/2.

how does this ad up to fifteen degenarate states?

You are doing as if there was only a single electron.

You must combine the two l=1 states to get the total orbital angular momentum.
Then you must combine the two s=1/2 states to get the total spin.
Now, you must make sure that you include only states that are antisymmetric.
 
  • #3
Thank you, With your help i solved it.
 
  • #4
nrqed said:
Now, you must make sure that you include only states that are antisymmetric.

Why do you only take in acount for the antisymmetric states?

Can someone give an exampel on how a antisymmteric states looks like for, 2 electrons and 3 electrons?

Thank you, Joqe
 

FAQ: LS-coupling for configurations with equivalent electrons

1. What is LS-coupling and how does it apply to configurations with equivalent electrons?

LS-coupling is a method of describing the electronic structure of an atom or molecule by considering the interactions between the spin (S) and orbital (L) angular momentum of the electrons. For configurations with equivalent electrons, LS-coupling takes into account the fact that the electrons have the same energy and therefore similar behavior.

2. How are the spin and orbital angular momenta related in LS-coupling for equivalent electron configurations?

In LS-coupling, the total angular momentum (J) is the vector sum of the spin and orbital angular momenta. For equivalent electron configurations, the spin and orbital angular momenta are coupled in such a way that they add up to the same value for all electrons in the configuration.

3. Can LS-coupling be used for configurations with non-equivalent electrons?

Yes, LS-coupling can be used for configurations with non-equivalent electrons, but it may not provide an accurate description of the electronic structure. In these cases, it may be necessary to use more advanced methods such as intermediate coupling.

4. Are there any other factors that can affect LS-coupling for equivalent electron configurations?

Yes, in addition to equivalent electron configurations, the strength of the spin-orbit interaction can also affect LS-coupling. This is because the spin-orbit interaction determines the energy difference between different levels of the same configuration, which can impact the overall behavior of the electrons.

5. How does LS-coupling contribute to the understanding of the electronic structure of atoms and molecules?

LS-coupling is a useful tool for predicting the energy levels and electronic transitions of atoms and molecules. It allows us to simplify the complex interactions between electrons and provides a framework for understanding the spectra and chemical properties of these systems.

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