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Spin. Griffiths tells me that particle spin is intrinsic angular momentum. This spin isn't actually analogous to the particle spinning in a classical manner, however. Then, later Griffiths says that a spinning charged particle has a magnetic moment. This doesn't make any sense to me, considering that we aren't actually considering the particle to be spinning (in a classical sense).

Even though the particle isn't actually 'spinning', the fact that there is an intrinsic angular momentum implies (by definition) that some sort of motion is taking place, and Maxwell's equations say that any moving charged particle creates a magnetic moment. So while the electron isn't spinning classically, there is some sort of motion going on that leads to the magnetic moment.

Is this magnetic moment perhaps similar but different in the same way that spin is 'similar but different' to classical mechanical spin? It seems like there are a great deal of things like this in quantum… it seems kind of like Griffiths is using a lot of classical terms to describe quantum mechanical processees – and like he says, don't take the analogy too far. There are two different kinds of magnetic moments – moments that are intrinsic to particles, like this electron, and moments that are due to the change in current or a flux type situation. (I say griffiths – obviously I mean this as the Quantum voice personified).

Its my understanding that the quantum and classical magnetic moments are one and the same.

“There are two different kinds of magnetic moments – moments that are intrinsic to particles, like this electron, and moments that are due to the change in current or a flux type situation.”

The intrinsic moment of the electron is due to the intrinsic motion implied by its angular momentum. This motion leads to the change in current/flux situation you mentioned. I have no idea what sort of actual motion the electron must have though and would be very interested to hear some theories.

Griffiths advises to not push the analogy too far: an electron is considered a point particle that doesn't seem to have any internal “structure” and that the spin “cannot be decomposed into orbital angular momenta of constituent parts.” As I see it, when you draw an electron with spin up or down as a dot with a magnetic moment arrow pointing up or down, that's really all you can say about how it's “spinning.”

Could we clear up the “eigenspinor” vs. eigenvector thing? I've read elsewhere that eigenspinors are not eigenvectors, but Griffiths seems to be using an eigenspinor for what I would call an eigenvector. But also as a hybrid of what look like eigenvectors. (I refer to pg 175). Could we have a clear and decisive deliniation of all these terms please? spinor, eigenspinor, etc. I'm sure I'm missing something… and I'm kind of tired… but…. y'all know what I mean.

I have no idea what an eigenspinor physically represents.

This is what I found on Wikipedia:

Eigenspinors are thought of as basis vectors representing the general spin state of a particle. Strictly speaking, they are not vectors at all, but in fact spinors.

Spinors are elements of a complex vector space introduced to expand the notion of spatial vector. They are needed because the full structure of the group of rotations in a given number of dimensions requires some extra number of dimensions to exhibit it. Specifically, spinors are geometrical objects constructed from a vector space endowed with a quadratic form, such as a Euclidean or Minkowski space, by means of an algebraic procedure, through Clifford algebras, or a quantization procedure. A given quadratic form may support several different types of spinors.

For a single spin 1/2 particle, they can be defined as the eigenvectors of the Pauli matrices.

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