LS-coupling for configurations with equivalent electrons

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SUMMARY

The discussion focuses on determining the fifteen degenerate states for two electrons in a np2 configuration under the central field approximation. The magnetic quantum numbers for the two electrons are defined as ml1, ml2, and ms1, ms2, where ml can take values of -1, 0, and 1, while ms can take values of -1/2 and 1/2. The combination of these states must adhere to the antisymmetry requirement, leading to the conclusion that only antisymmetric states are valid for this configuration. The participants clarify the necessity of combining the orbital angular momentum and total spin states to arrive at the correct count of degenerate states.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically angular momentum.
  • Familiarity with quantum numbers, including magnetic quantum numbers (ml) and spin quantum numbers (ms).
  • Knowledge of antisymmetry in quantum states, particularly for fermions.
  • Basic grasp of the central field approximation in quantum mechanics.
NEXT STEPS
  • Study the principles of angular momentum coupling in quantum mechanics.
  • Learn about antisymmetric wave functions for multiple fermions.
  • Explore the central field approximation and its applications in atomic physics.
  • Investigate the implications of quantum numbers in electron configurations.
USEFUL FOR

This discussion is beneficial for students and professionals in quantum mechanics, particularly those studying atomic structures, electron configurations, and angular momentum coupling. It is especially relevant for physicists and chemists working with multi-electron systems.

damaks
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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?
 
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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.
 
Thank you, With your help i solved it.
 
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
 

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