Ground state: singlet or triplet

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SUMMARY

The ground state of two 1s electrons is definitively a singlet, while the ground state of two 2p electrons can be either a singlet or a triplet. Determining the ground state type relies on analyzing the symmetry group of the theory and identifying operators that strongly commute with the Hamiltonian. This method aligns with Hund's rules, which provide a framework for understanding electron configurations in atoms.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of electron configurations
  • Familiarity with symmetry groups in physics
  • Knowledge of Hamiltonian operators
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Students and professionals in quantum mechanics, physicists studying atomic structure, and anyone interested in the principles of electron configurations and their ground states.

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In my book it is mentioned that for the two 1s electrons the ground state is the singlet while for the two 2p electrons the ground state could be either singlet or triplet.
Generally how can you determine whether the ground state is singlet or triplet?
 
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By looking at the symmetry group of the theory: looking for all operators strongly commuting with the Hamiltonian.
 

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