4: The Spin-1/2 Particle
- Page ID
- 56756
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Moving electric charges, or currents, interact with magnetic fields; they both respond to them, and create them. You know from Section 3.3 that a spinning ball has angular momentum. If that spinning ball is also charged, that means that, effectively, there are currents associated with the ball. Suppose that the charge is spread uniformly throughout the ball. The charges right along the axis aren’t moving, and so wouldn’t respond to or create magnetic fields. However, all of the bits of ball that aren’t right along the axis are making a circle around the axis. As such, they are moving charges, and they will respond to a magnetic field.
This may seem like a completely unfounded leap, or it may seem like an obvious leap, but from this observation, we can say that a particle that has both charge and angular momentum will respond to magnetic fields.
- 4.1: Particles in Quantum Mechanics
- When we talk about a “particle” in quantum mechanics, we mean something that behaves as if it were just a single body. However, we are often also talking about a particle as it is understood in the Standard Model of Particle Physics. In the Standard Model, a fundamental particle is something that is effectively a mathematical point. As far as we can tell, the fundamental particles have no spatial extent. The most common everyday example of a particle from the Standard Model is the electron.
- 4.2: Measuring Electron Spin- the Stern-Gerlach Experiment
- If a particle that has both charge and angular momentum interacts with magnetic fields, and if we know what that charge is through other experiments, then we ought to be able to figure out the angular momentum of that particle by some sort of experiment involving magnetic fields. If a particle with charge and angular momentum moves through a nonuniform magnetic field, it will be pulled along the direction of the nonuniformity based on the projection or component of its angular momentum along the