Hund's rule and angular momentum coupling

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SUMMARY

The discussion centers on Hund's second rule concerning angular momentum coupling, specifically the relationship between the total angular momentum L and its z-component L_z. Participants clarify that while L_z represents the projection of angular momentum along the z-axis, L is defined as the maximum eigenvalue of the L_z operator. The confusion arises from the distinction between the eigenvalues of the L_z operator and the L^2 operator, where L(L+1) is the eigenvalue associated with L^2, not L_z.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with angular momentum operators in quantum mechanics
  • Knowledge of eigenvalues and eigenvectors in linear algebra
  • Basic grasp of Hund's rules in atomic physics
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  • Study the mathematical formulation of angular momentum in quantum mechanics
  • Learn about the implications of eigenvalues in quantum systems
  • Explore the differences between L_z and L^2 operators
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daudaudaudau
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Hi.

In Hund's second rule, it seems that we calculate the value of L simply by summing the [itex]L_z[/itex] components of the individual electrons. But L has to do with the eigenvalue of the L^2 operator, i.e. the eigenvalue is L(L+1). So how can this be correct?
 
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L is the maximum eigenvalue of L_z.
L(L+1) is the eigenvalue of a different operator, L^2.
 
Meir Achuz said:
L is the maximum eigenvalue of L_z.
L(L+1) is the eigenvalue of a different operator, L^2.

Yeah that is exactly my point. We know that that L_z has some particular value. Now why is L=L_z ?
 

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