Spin and orbital magnetic moments?

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Discussion Overview

The discussion centers around the nature of the total magnetic moment of an electron, specifically the contributions from spin and orbital magnetic moments. Participants explore the quantum mechanical implications of orbital magnetic moments, particularly in the context of the Stern-Gerlach experiment and the quantization of angular momentum.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question the realism of the orbital magnetic moment in quantum mechanics, noting that electrons do not have classical trajectories.
  • One participant points out that the net orbital angular momentum of the 47 electrons in a silver atom is zero, with the total angular momentum arising solely from the spin of the outermost electron.
  • Another participant emphasizes that orbital angular momentum is quantized and relates to the quantization of the magnetic moment, suggesting that this quantization is a real phenomenon that can be measured.
  • One contribution reiterates the concern about the implications of orbital magnetic moments on the results of the Stern-Gerlach experiment, questioning why the paths do not appear more spread out if both spin and orbital moments are considered.
  • A later reply asserts that the orbital magnetic moment is realistic, referencing its mathematical formulation and its contribution to energy level shifts in stationary states of the hydrogen atom.

Areas of Agreement / Disagreement

Participants express differing views on the validity and implications of orbital magnetic moments in quantum mechanics. There is no consensus on whether the orbital magnetic moment is a realistic concept within the framework discussed.

Contextual Notes

Some limitations include the dependence on definitions of angular momentum and magnetic moments, as well as the unresolved nature of how these concepts apply to experimental observations like the Stern-Gerlach experiment.

pivoxa15
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The books said that total magnetic moment of an electron is spin + orbital magnetic moment.

But is the orbital magnetic moment realistic quantum mechanically? I thought electrons doesn't have a trajectory. The Stern Garlach experiment showed that silver atoms only split into two paths after being in a magnetic field. But if orbital magnetic moment was also present then shouldn't there be less distinction in that the paths may have been more spread out or random.
 
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The net orbital angular momentum of the 47 electrons in a silver atom is zero, and their spins "pair up" so the total angular momentum (orbital + spin) comes only from the spin of the outermost electron.
 
pivoxa15 said:
The books said that total magnetic moment of an electron is spin + orbital magnetic moment.

But is the orbital magnetic moment realistic quantum mechanically? I thought electrons doesn't have a trajectory. The Stern Garlach experiment showed that silver atoms only split into two paths after being in a magnetic field. But if orbital magnetic moment was also present then shouldn't there be less distinction in that the paths may have been more spread out or random.
Orbital angular momentum is also quantized. If an atom has both S and L, then J=L+S. (QM addition. This is called "L-S coupling".)
J is quantized and would determine the SG splitting.
 
The angular momentum of an electron is also quantised and a real phenomena in that it can be measured (although only one component at a time). Classically moving charges generate a magnetic field so that is why we associate an orbital magnetic moment to an electron in an atom. But the angular momentum is quantised and that is why the magnetic moment is also quantised.
 
pivoxa15 said:
The books said that total magnetic moment of an electron is spin + orbital magnetic moment.

But is the orbital magnetic moment realistic quantum mechanically? I thought electrons doesn't have a trajectory. The Stern Garlach experiment showed that silver atoms only split into two paths after being in a magnetic field. But if orbital magnetic moment was also present then shouldn't there be less distinction in that the paths may have been more spread out or random.

Well, since it's given by

\hat{\mu}_{orb} \sim \hat{\vec{L}}\cdot \vec{B},

i'd say it's pretty realistic...

Daniel.

P.S. For l\neq 0 stationary states of the H-atom it gives a contribution to the shifting of the normal energy levels.
 

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