Why does the electron have a magnetic moment?

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SUMMARY

The magnetic moment of the electron is fundamentally linked to its intrinsic spin, as described by the Pauli equation, rather than being solely derived from classical concepts of charge currents. While the Dirac equation provides a relativistic framework for understanding this phenomenon, the nonrelativistic Pauli equation suffices to include the magnetic moment due to its inherent spin characteristics. This discussion clarifies that the electron's magnetic moment is not merely a result of its rotation and charge but is a fundamental property of its quantum mechanical nature.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the Pauli equation
  • Knowledge of the Dirac equation
  • Concept of electron spin
NEXT STEPS
  • Study the implications of the Pauli equation in quantum mechanics
  • Explore the Dirac equation and its applications in particle physics
  • Investigate the concept of spin and its role in quantum mechanics
  • Learn about magnetic moments in other particles and their significance
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Physicists, students of quantum mechanics, and anyone interested in the fundamental properties of subatomic particles will benefit from this discussion.

carllacan
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Hi.

I thought magnetic moment arose from closed loops of charge currents. How does then the angular momentum of the electron produce a magnetic moment? I mean, the electron is not a loop.

Am I wrong in my initial assumption or am I understanding things too "classically"?

Thanks.
 
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You are thinking too classically. The electron's magnetic moment arises from the relativistic QM Dirac equation for the electron.
 
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You don't need Dirac's equation to derive the magnetic moment of the electron. Pauli's nonrelativistic equation will suffice.
 
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I see. Then saying that the magnetic moment arises from its rotation and its charge is just oversimplifying things, right?
 
Right. Pauli's equation can include the moment, but does not derive it as a necessity.
 
Pauli's equation always includes the magnetic moment, because it automatically includes the spin.
 

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