Undergrad What do you need to establish that spin is conserved?

[Old Person]

TL;DR

What do you need to establish that spin is a conserved quantity?

Hi.

Question as in the summary.
Spin has no obvious classical interpretation but it is often a conserved quantity and considered as some sort of angular momentum. What do you need to establish that spin is a conserved quantity? I'm finding references to situations where spin is not a conserved quantity in general but only in some processes. Hence, what is needed to assert conservation?

Any replies or references to existing discussions or proofs would save me time and be appreciated. Thank you for your time.

 

[PeterDonis]

Spin has no obvious classical interpretation but it is often a conserved quantity and considered as some sort of angular momentum.

No, spin by itself is not "often" a conserved quantity. Total angular momentum is the conserved quantity. Only in situations where orbital angular momentum is either identically zero or is conserved on its own can spin be considered a conserved quantity by itself.

As for spin being "some sort of" angular momentum, that's much too vague. Spin is whatever part of total angular momentum is not orbital angular momentum. See, for example, Ballentine, Chapter 7.

 

[Old Person]

Thank you. I'll look for that when I get to a library.
Found: "Quantum Mechanics: A Modern Development" by Leslie E. Ballentine.
No great need to reply - I'll assume it's that book unless you say otherwise.

 

[PeterDonis]

Found: "Quantum Mechanics: A Modern Development" by Leslie E. Ballentine.

Yes, that's it.