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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).

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).

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.

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.”

Multiple sources say that there are two kinds of spin. There may be motion of the electron, but this is not necessarily where the spin comes from. Spin for the electron is an intrinsic property and part of the description of an electron. Unlike the other type of spin which changes and is not an intrinsic property. I agree with Hilbert. I think this is getting pushed too far.

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.

Eigenspinors have a similar place as do rotational quantities in classical mechanics do(for instance omega, which is indicated by the axis it is spinning on). Although rotational quantities in classical mechanics are given a direction, by the axis on which it spins around, this does not satisfy the definition of a vector, so we let it be a pseudo-vector. Sometimes we call rotational quantities vectors, because it fits for that situation and we forget to add that is actually on vector like, which is given by “pseudo”.

Similarly, in QM, eigenvectors found from our spin operators are pseudo-like in nature, to that of its close relative of the eigenstates, which we get from non-spin operators. We call this a Eigenspinors or just Spinors. I don't know what the difference is between the eigenstates and eignespinors and I don't get anything from the classical analogue, since spin isn't the actual “spin” we talk about in classical mechanics. But I think the subtle difference between spinors and eigenstates are don't affect us in the topic we are discussing in Griffths, which is why he calls it a eigenstate, like we calling a rotational quantity in classical mechanics a “vector”.

Hope that helps, there is a lot of math behind this, but I don't think it is really important.

I looked at how Griffths calculated the probability when given a state, but how do you figure out the coefficients of psi+ and psi-? Without this, I am at a lost of calculated probability for certain spin states.

I'm looking for a better way to conceptualize what we are doing in class, can anyone help me understand how a particle can have 1/2 of a spin? I know “spin” is a more or less a made up term when it comes to electrons or gravitons and the like, but why don't we just multiply all the spins by 2 and make it easier to understand classically (which is the reason for calling it spin in the first place, if I'm not mistaken)? This is confusing because how can something have half a spin? I guess it's all relative because gravitons have spin of 2, which also makes no sense. Is there a specific reason for there being 1/2 spins instead of just calling everything by twice that?

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