How are Magnetic Fields described in Quantum Mechanics?

[boderam]

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.

 

[Eynstone]

Spin magnetic moment is internal.Not all magnetic fields are generated by spin.

 

[Born2bwire]

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.

 

[boderam]

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)?

 

[Born2bwire]

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.

 

[boderam]

Ok, thank you very much.