Full Basis of Angular Momentum Eigenstates

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SUMMARY

The discussion focuses on the full basis of angular momentum eigenstates for an atom with two unpaired electrons in s-orbitals. It establishes that since the orbital angular momentum (l) is zero for s-orbitals, only the spin angular momentum needs to be considered. The relevant equations for angular momentum, including the definitions of lx, ly, lz, l+, and l-, are provided but the initial poster expresses uncertainty about how to proceed with the solution.

PREREQUISITES
  • Understanding of angular momentum in quantum mechanics
  • Familiarity with s-orbitals and their properties
  • Knowledge of spin angular momentum concepts
  • Proficiency in using angular momentum operators
NEXT STEPS
  • Study the mathematical representation of spin angular momentum
  • Learn about the coupling of angular momentum in quantum systems
  • Explore the implications of s-orbitals on total angular momentum
  • Investigate the use of angular momentum eigenstates in quantum mechanics
USEFUL FOR

Students and researchers in quantum mechanics, particularly those focusing on angular momentum and atomic structure, will benefit from this discussion.

Werner Rontgen
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Homework Statement


Consider the case of an atom with two unpaired electrons, both of which are in s-orbitals. Write the full basis of angular momentum eigenstates representing the coupled and uncoupled representations

Homework Equations


l=r×p
lx=ypz-zpy
ly=zpx-xpz
lz=xpy-ypx

l+=lx+ily
l-=lx-ily

The Attempt at a Solution


I am not sure how to start. If I am correct I already wrote a complete basis for l.
 
Werner Rontgen said:

Homework Statement


Consider the case of an atom with two unpaired electrons, both of which are in s-orbitals. Write the full basis of angular momentum eigenstates representing the coupled and uncoupled representations

Homework Equations


l=r×p
lx=ypz-zpy
ly=zpx-xpz
lz=xpy-ypx

l+=lx+ily
l-=lx-ily

The Attempt at a Solution


I am not sure how to start. If I am correct I already wrote a complete basis for l.

Well, the problem statement says that the electrons are in "s-orbitals". That means that the orbital angular momentum is zero. So the only relevant angular momentum is spin angular momentum, I would think.
 

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