# Does quantum spin suggest particles have extent? [duplicate]

I have taken a few quantum mechanics courses recently, which has involved quite a bit of work with quantum spin. The professors keep saying that spin is analogous to a classical body spinning on its axis. However they always make sure we clearly understand this isn't exactly what is happening, because quantum mechanics deals with point particles. Because they don't have extent, there is nothing 'poking out' from the centre of the particle that can spin around the axis.

However it seems to me that if particles in quantum mechanics have this property, it would suggest that they might not be point particles after all, and have some 'size'. No doubt this has been investigated quite thoroughly.

I was wondering then why intrinsic spin isn't considered evidence that particles aren't just points, and have 'size' or 'shape'?

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## 1 Answer

Spin is angular momentum, but for fermions it has the wrong quantization to be $\mathbf{r} \times \mathbf{p}$.

The quantization conditions for any extended rigid body in rotation end up requiring that the total angular momentum be an integer times $\hbar$ (note that the units of $\hbar$ are compatible with those of angular momentum). This means that the half-integer spin of a fermion can't represent the rotation of an extended massive body.

• Great, this is just what I was after. Do you happen do know where I could read about that in a little more detail? – leob Oct 24 '17 at 0:21
• Any upper-division or graduate quantum mechanics text should cover it. I'd say the prerequisites are an understanding of classical angular momentum as a vector quantity and quantum mechanics up to the ladder-operator version of the harmonic oscillator. – dmckee Oct 24 '17 at 0:24