Spin 1/2 particles and magnetic fields

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SUMMARY

When a spin 1/2 particle is placed in a magnetic field, it does not simply align with or against the field; instead, it undergoes precession due to the relationship between its magnetic dipole moment and angular momentum. The magnetic dipole moment, defined as μ = γL, leads to the phenomenon known as Larmor Precession, where the spin vector precesses around the magnetic field direction rather than aligning directly with it. The terms "spin up" and "spin down" refer to the z-component of the spin vector, quantified as +ħ/2 or -ħ/2, respectively, rather than the orientation of the magnetic moment. This intrinsic property of particles, such as electrons, is influenced by external forces and the time evolution of spinors.

PREREQUISITES
  • Understanding of quantum mechanics, specifically spin and angular momentum.
  • Familiarity with magnetic dipole moments and their relation to magnetic fields.
  • Knowledge of Larmor Precession and its implications in quantum systems.
  • Basic grasp of quantum state notation and expectation values.
NEXT STEPS
  • Study the concept of Larmor Precession in detail, including mathematical formulations.
  • Explore the implications of spin in quantum mechanics, focusing on spinors and their time evolution.
  • Investigate the relationship between magnetic moments and angular momentum in quantum particles.
  • Learn about applications of spin and magnetic fields in technologies like Magnetic Resonance Imaging (MRI).
USEFUL FOR

Physicists, quantum mechanics students, and anyone interested in the behavior of spin 1/2 particles in magnetic fields will benefit from this discussion.

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I was told that if you put a spin 1/2 particle in a magnetic field, it will align with or against the field. But some places it also says that it will precess around the field. Which one is right?
 
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If the magnetic dipole of that particle is constant (as is in the classical case) then the dipole will allign with the magnetic field. If the magnetic dipole is proportional to the angular momentum, as is the case with actual particles \mu=\gamma*L Then the dipole (and therefore the spin) can no longer align with the magnetic field, and will precess around it (Larmer Precession).
 
So the spin doesn't *really* align with the magnetic field, then, it just precesses around it. So what do spin 'up' and spin 'down' really refer to? To whether the magnetic moment is pointed towards the direction of the field or away from it, but not parallel or antiparallel? I guess that would make sense.
 
Spin up and spin down are not defined using magnetic moments. They usually mean the z-component of the spin vector (expectation) is +hbar/2 or -hbar/2 for up or down respectively.
 
Matterwave said:
Spin up and spin down are not defined using magnetic moments. They usually mean the z-component of the spin vector (expectation) is +hbar/2 or -hbar/2 for up or down respectively.

So I had it backwards? The spin is intrinsic, and the magnetic moment is defined using the spin - since spin is a type of angular momentum.

So if I put a spin 1/2 particle in a magnetic field, whether or not the spin vector points towards the field or away from it determines whether or not the magnetic dipole moment precesses towards or away from the direction of the magnetic field?
 
The spin is an intrinsic property of a particle (electron is 1/2, photon is 1, etc). But think of this "spin" as the "total spin". I.e. it is like the magnitude of the spin vector. The spin's "direction" and what not is determined by external "forces" and the time evolution of the spinors.
 
Now that makes sense! (-in so much as spin is sensible) Thanks!
 
precessing particles emit radio waves until they stop precessing.
en.wikipedia.org/wiki/Magnetic_resonance_imaging
 

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