How are Magnetic Fields described in Quantum Mechanics?

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Discussion Overview

The discussion centers on the nature of magnetic fields in the context of quantum mechanics, exploring how these fields arise from various properties of electrons, including spin and orbital momentum. Participants examine the relationship between classical and quantum descriptions of magnetism, as well as the appropriate theoretical frameworks for understanding these phenomena.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that ferromagnetism is related to the spin behavior of many electrons and questions if all magnetic fields arise from spin.
  • Another participant asserts that not all magnetic fields are generated by spin, indicating that the spin magnetic moment is internal.
  • It is proposed that the spin only accounts for part of magnetism, with additional contributions from the orbital momentum of electrons and classical charge acceleration.
  • A participant outlines a conceptual framework for magnetic fields arising from an electron, suggesting that the total magnetic field can be viewed as a sum of contributions from orbital angular momentum, spin magnetic moment, and a component derived from the electron's velocity.
  • One reply challenges the use of the relativistic Biot-Savart law, suggesting that the Jefimenko equations would be more appropriate for describing magnetic sources due to a charge, while acknowledging that the proposed framework could serve as a good approximation.

Areas of Agreement / Disagreement

Participants express differing views on the contributions to magnetic fields, with some emphasizing the role of spin and others highlighting the importance of orbital momentum and classical effects. The discussion remains unresolved regarding the complete characterization of magnetic fields in quantum mechanics.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the relationship between quantum mechanics and classical electromagnetism, as well as the applicability of different equations to describe magnetic fields.

boderam
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Apologies for any vagueness or ignorance here (and lack of citations) but I remember reading that ferromagnetism arises from spin behavior of many electrons. So in a broader sense, are all magnetic fields arising from spin? I am trying to understand how magnetic fields can be viewed at the quantum level, i.e. the total magnetic field arising from an electron obeying the Schrödinger equation.
 
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Spin magnetic moment is internal.Not all magnetic fields are generated by spin.
 
The spin only accounts for a part of magnetism. There is also a magnetic moment that arises from the orbital momentum of the electron which is akin to a classical current loop. And of course we still need to be able to produce magnetic fields in the classical sense by the acceleration of charges and with currents. But in terms of quantum mechanics, electromagnetism is not described by the Schroedinger equation, which is a non-relativistic mechanical equation. It requires a quantum field theory like QED. We can use electromagnetism in the Schroedinger equation by describing it as a potential. This is what we do when we want to look at the interaction of spins and moments. But these fields are still treated as classical fields.
 
Ok, so in other words can we say a magnetic field, being that it is a result of moving charge is composed of three things:

1. the quantum orbital angular momentum L = r x p = B_1
2. the spin magnetic moment written as B_2
3. a component derived from the velocity of the actual electron using a relativistic form of Biot-Savart = B_3

And B_1 + B_2 + B_3 = total B due to one electron (minus some relativistic corrections from L and spin)?
 
Last edited:
Not relativistic Biot-Savart as Biot-Savart is magnetostatic. The appropriate expression would be the Jefimenko equations which include both retardation and time-variation. But yeah, I guess that would be a good approximation of the magnetic sources due to a charge.
 
Ok, thank you very much.
 

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