How are Magnetic Fields described in Quantum Mechanics?

In summary, all magnetic fields arise from spin. Some fields are generated by spin, while others are generated by other factors such as orbital momentum.
  • #1
boderam
24
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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 Schrodinger equation.
 
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  • #2
Spin magnetic moment is internal.Not all magnetic fields are generated by spin.
 
  • #3
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.
 
  • #4
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)?
 
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  • #5
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.
 
  • #6
Ok, thank you very much.
 

1. What is a magnetic field in the context of quantum mechanics?

A magnetic field in quantum mechanics is a region of space where charged particles, such as electrons, experience a force due to their motion. It is described by a vector field that indicates the direction and strength of the force at each point in space.

2. How are magnetic fields described mathematically in quantum mechanics?

In quantum mechanics, magnetic fields are described using the vector potential, which is related to the magnetic field through the equation B = ∇ x A, where B is the magnetic field and A is the vector potential. This mathematical description allows us to calculate the force on a charged particle in a magnetic field.

3. How do magnetic fields interact with particles in quantum mechanics?

In quantum mechanics, particles with an electric charge have a property called spin, which is related to their magnetic moment. When a particle with spin moves through a magnetic field, it experiences a torque, causing it to align with the direction of the field. This interaction is the basis for many quantum phenomena, such as the Zeeman effect and electron spin resonance.

4. How do magnetic fields affect the behavior of particles in quantum mechanics?

Magnetic fields can have a significant impact on the behavior of particles in quantum mechanics. They can alter the energy levels of atoms, leading to the splitting of spectral lines, and they can also affect the trajectories of particles, causing them to move in curved paths. Additionally, magnetic fields can influence the spin states of particles, which can have implications for quantum computing and information processing.

5. Are there any limitations to how magnetic fields are described in quantum mechanics?

While quantum mechanics provides a robust framework for describing magnetic fields, it does have some limitations. For example, the theory does not account for the effects of gravity on magnetic fields, and it does not fully explain the origin of magnetic fields in the universe. Additionally, quantum mechanics is a non-relativistic theory, meaning it does not incorporate the principles of special relativity, which can be problematic when dealing with high-energy particles.

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