# Metaphor for orbital angular momentum?

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1. Aug 7, 2015

### NanaToru

I've been tutoring for chemistry and someone asked me to clarify the difference of spin angular momentum and orbital angular momentum without math.

I was trying to think of a metaphor, but I wanted to make sure it's a fair one--the spin angular momentum is like Earth rotating on its own axis and orbital angular momentum of an electron in an orbital is analogous to the rotation of the Earth around the Sun. Of course this ignores a lot of other implications like resultant magnetic momentum, but it was the simplest one I could come up with.

Is this fair? I"m worried that they might get into their head that electrons then spin on a specific path like the Bohr model, but I'm not sure what else to compare it to. And of course this only applies to hydrogen like species but again, I was a bit on the spot... I'd love to give them a better metaphor.

2. Aug 7, 2015

### blue_leaf77

Orbital angular momentum does have classical analog in that they can be represented as an operator product
$$\hat{\mathbf{L}} = \hat{\mathbf{r}} \times \hat{\mathbf{p}}$$
Which also holds in classical dynamics, such as that in planet's orbit. So it's a relatively fair analogy and won't be that misleading for a mere metaphor.
Unfortunately the spin angular momentum has no classical analog, the spin operators (to the best of my knowledge) cannot be represented by any other operators which have classical analogue as is the case for orbital angular momentum being a vector product between position and momentum vectors. It may be safer to just "dictate" to your student that spin angular momentum is just there for every particle, i.e. there happened to be another angular momentum aside from orbital angular momentum in the quantum world, this being one of the distinguishing trademarks of quantum mechanics as opposed to classical mechanics. Forcing the notion that spin in QM is analogue to the spin in CM won't get your student anywhere in understanding even the basic nature of the former case.