How does magnetism work in QM?

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SUMMARY

Magnetism in quantum mechanics (QM) is fundamentally linked to the spin state of electrons, which dictates the magnetic properties of materials. Unlike classical mechanics (CM), where field lines and vector fields are clearly defined, QM introduces uncertainty in the magnetic field values at every point in space. This uncertainty manifests as probability distributions for the magnetic field components, which can be analyzed through their averages and variances. The classical limit occurs when these distributions are sharply peaked, allowing for simplifications in modeling the magnetic field.

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  • Understanding of electron spin and its role in magnetism
  • Familiarity with quantum mechanics principles
  • Knowledge of classical mechanics concepts, particularly field lines and vector fields
  • Basic grasp of probability distributions and uncertainty relations
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S Beck
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Electrons' spin state is responsible for magnetism inside a magnet. Two magnets interact at a distance, but what about the space between and around the two magnetic objects? In CM there are field lines and vector fields, but what is actually happening at the QM level?
 
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In quantum mechanics, the values of the magnetic field are uncertain. At every point in space, you may talk about the probability distribution satisfied by the three components of the magnetic field - their average, their variance, etc. There will also be uncertainty relations, say between the components of the magnetic and electric fields.

The classical limit is when these probability distributions are highly peaked about their mean, so you can just ignore them and model the system by the mean magnetic field everywhere.
 
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S Beck said:
but what is actually happening at the QM level?
Beware! asking questions like this is likely to lead you down a rabbit hole into a maze of twisty little passages, all alike. :eek:
 
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